## Vershik, Anatoliĭ Moiseevich

Compute Distance To:
 Author ID: vershik.anatoli-m Published as: Vershik, A. M.; Vershik, A.; Vershik, Anatoly; Vershik, Anatoly M.; Vershik, Anatolii M.; Vershik, Anatoli M.; Vershik, Anatol M.; Vershik, Anatolii; Vershik, Anatolij; Vershik, Anatoli; Vershik, A. M Homepage: http://www.pdmi.ras.ru/~vershik External Links: MGP · ORCID · Wikidata · ResearchGate · Math-Net.Ru · dblp · GND · IdRef · theses.fr
 Documents Indexed: 373 Publications since 1958, including 2 Books 48 Contributions as Editor · 3 Further Contributions Biographic References: 3 Publications Co-Authors: 281 Co-Authors with 257 Joint Publications 7,136 Co-Co-Authors
all top 5

all top 5

all top 5

### Fields

 103 Group theory and generalizations (20-XX) 80 Measure and integration (28-XX) 78 Combinatorics (05-XX) 76 Dynamical systems and ergodic theory (37-XX) 63 History and biography (01-XX) 63 Probability theory and stochastic processes (60-XX) 57 Topological groups, Lie groups (22-XX) 49 General and overarching topics; collections (00-XX) 45 Functional analysis (46-XX) 28 Number theory (11-XX) 26 Global analysis, analysis on manifolds (58-XX) 25 Operations research, mathematical programming (90-XX) 24 Operator theory (47-XX) 22 Calculus of variations and optimal control; optimization (49-XX) 21 Computer science (68-XX) 20 Numerical analysis (65-XX) 20 Quantum theory (81-XX) 19 Nonassociative rings and algebras (17-XX) 18 Differential geometry (53-XX) 18 General topology (54-XX) 15 Associative rings and algebras (16-XX) 15 Abstract harmonic analysis (43-XX) 14 Convex and discrete geometry (52-XX) 11 Statistical mechanics, structure of matter (82-XX) 8 Algebraic geometry (14-XX) 8 Manifolds and cell complexes (57-XX) 7 Partial differential equations (35-XX) 7 Mechanics of particles and systems (70-XX) 5 Order, lattices, ordered algebraic structures (06-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Geometry (51-XX) 3 $$K$$-theory (19-XX) 3 Approximations and expansions (41-XX) 2 Mathematical logic and foundations (03-XX) 2 Real functions (26-XX) 2 Special functions (33-XX) 2 Fluid mechanics (76-XX) 2 Relativity and gravitational theory (83-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Information and communication theory, circuits (94-XX) 1 Category theory; homological algebra (18-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Algebraic topology (55-XX) 1 Biology and other natural sciences (92-XX)

### Citations contained in zbMATH Open

284 Publications have been cited 3,065 times in 1,965 Documents Cited by Year
Random walks on discrete groups: Boundary and entropy. Zbl 0641.60009
Kaimanovich, V. A.; Vershik, A. M.
1983
Asymptotics of the Plancherel measure of the symmetric group and the limiting form of Young tableaux. Zbl 0406.05008
Vershik, A. M.; Kerov, S. V.
1977
Statistical mechanics of combinatorial partitions, and their limit shapes. Zbl 0868.05004
Vershik, A. M.
1996
Nonholonomic dynamical systems, geometry of distributions and variational problems. Zbl 0797.58007
Vershik, A. M.; Gershkovich, V. Ya.
1987
A new approach to representation theory of symmetric groups. Zbl 0959.20014
Okounkov, Andrei; Vershik, Anatoly
1996
Asymptotic theory of characters of the symmetric group. Zbl 0507.20006
Vershik, A. M.; Kerov, S. V.
1982
Characters and factor representations of the infinite symmetric group. Zbl 0534.20008
Vershik, A. M.; Kerov, S. V.
1981
Asymptotics of maximal and typical dimensions of irreducible representations of a symmetric group. Zbl 0592.20015
Vershik, A. M.; Kerov, S. V.
1985
Harmonic analysis on the infinite symmetric group. Zbl 1057.43005
Kerov, Sergei; Olshanski, Grigori; Vershik, Anatoly
2004
Characters and factor representations of the infinite unitary group. Zbl 0524.22017
Vershik, A. M.; Kerov, S. V.
1982
Representations of the group of diffeomorphisms. Zbl 0337.58003
Vershik, A. M.; Gel’fand, I. M.; Graev, M. I.
1975
Dynamic theory of growth in groups: Entropy, boundaries, examples. Zbl 0991.37005
Vershik, A. M.
2000
Harmonic analysis on the infinite symmetric group. A deformation of the regular representation. Zbl 0796.43005
Kerov, Serguei; Olshanski, Grigori; Vershik, Anatoli
1993
Limit measures arising in the asymptotic theory of symmetric groups. I. Zbl 0375.60007
Vershik, A. M.; Shmidt, A. A.
1977
Adic models of ergodic transformations, spectral theory, substitutions, and related topics. Zbl 0770.28013
Vershik, A. M.; Livshits, A. N.
1992
An infinite-dimensional analogue of the Lebesgue measure and distinguished properties of the gamma process. Zbl 0990.60053
Tsilevich, Natalia; Vershik, Anatoly; Yor, Marc
2001
$$C^*$$-algebras of irreversible dynamical systems. Zbl 1104.46037
Exel, R.; Vershik, A.
2006
The characters of the infinite symmetric group and probability properties of the Robinson-Schensted-Knuth algorithm. Zbl 0584.05004
Kerov, Sergei V.; Vershik, Anatol M.
1986
Ergodic unitarily invariant measures on the space of infinite Hermitian matrices. Zbl 0853.22016
Ol’shanskij, Grigorij; Vershik, Anatolij
1996
Decreasing sequences of measurable partitions and their applications. Zbl 0238.28011
Vershik, A. M.
1970
Totally nonfree actions and the infinite symmetric group. Zbl 1294.37004
Vershik, A. M.
2012
Uniform algebraic approximation of shift and multiplication operators. Zbl 0484.47005
Vershik, A. M.
1981
Arithmetic construction of sofic partitions of hyperbolic toral automorphisms. Zbl 0915.58077
Kenyon, Richard; Vershik, Anatoly
1998
Long history of the Monge-Kantorovich transportation problem. Zbl 1284.01041
Vershik, A. M.
2013
Description of invariant measures for the actions of some infinite- dimensional groups. Zbl 0324.28014
Vershik, A. M.
1974
$$BC$$-type interpolation Macdonald polynomials and binomial formula for Koornwinder polynomials. Zbl 0941.17005
Okounkov, Andrei; Vershik, Anatoly
1998
Ergodic properties of the Erdős measure, the entropy of the goldenshift, and related problems. Zbl 0916.28012
Sidorov, Nikita; Vershik, Anatoly
1998
Nonfree actions of countable groups and their characters. Zbl 1279.37004
Vershik, A. M.
2011
Reduction of nonholonomic variation problems to isoperimetric ones and connections in principal bundles. Zbl 0734.49023
Vershik, A. M.; Granichina, O. A.
1991
Large deviations for integer partitions. Zbl 0972.60006
Dembo, A.; Vershik, A.; Zeitouni, O.
2000
Differential geometry and Lagrangian mechanics with constraints. Zbl 0243.70014
Vershik, A. M.; Faddeev, L. D.
1972
The universal Urysohn space, Gromov metric triples and random metrics on the natural numbers. Zbl 1005.53036
Vershik, A. M.
1998
Some isometry groups of the Urysohn space. Zbl 1108.54027
Cameron, P. J.; Vershik, A. M.
2006
Representations of the group $$\text{SL}(2, R)$$, where $$R$$ is a ring of functions. Zbl 0288.22005
Vershik, A. M.; Gel’fand, I. M.; Graev, M. I.
1973
A theorem on the Markov periodic approximation in ergodic theory. Zbl 0559.47006
Vershik, A. M.
1985
The Kantorovich metric: the initial history and little-known applications. Zbl 1090.28009
Vershik, A. M.
2006
The limit shape of convex lattice polygons and related topics. Zbl 0848.52004
Vershik, A. M.
1994
Does there exist a Lebesgue measure in the infinite-dimensional space? Zbl 1165.28003
Vershik, A. M.
2007
Lagrangian mechanics in invariant form. Zbl 0518.58015
Vershik, A. M.; Faddeev, L. D.
1975
Factorial representations of path groups. Zbl 0522.22013
Albeverio, Sergio; Høegh-Krohn, Raphael; Testard, Daniel; Vershik, A.
1983
Asymptotic behavior of the number of faces of random polyhedra and the neighborliness problem. Zbl 0791.52011
Vershik, A. M.; Sporyshev, P. V.
1992
The word and geodesic problems in free solvable groups. Zbl 1207.20026
Myasnikov, A.; Roman’kov, V.; Ushakov, A.; Vershik, A.
2010
Multivalued mappings with invariant measure (polymorphisms) and Markov operators. Zbl 0408.28014
Vershik, A. M.
1977
On the number of convex lattice polytopes. Zbl 0772.52010
Bárány, I.; Vershik, A. M.
1992
On an infinite-dimensional group over a finite field. Zbl 1089.22006
Vershik, A. M.; Kerov, S. V.
1998
Locally semisimple algebras. Combinatorial theory and the $$K_ 0$$- functor. Zbl 0623.46036
Vershik, A. M.; Kerov, S. V.
1987
The Grothendieck group of infinite symmetric group and symmetric functions (with the elements of the theory of $$K_ 0$$-functor of AF- algebras). Zbl 0723.20005
Vershik, A. M.; Kerov, S. V.
1990
Linearly rigid metric spaces and the embedding problem. Zbl 1178.46016
Melleray, J.; Petrov, F. V.; Vershik, A. M.
2008
Random metric spaces and universality. Zbl 1065.60005
Vershik, A. M.
2003
Amenability and approximation of infinite groups. Zbl 0533.22007
Vershik, A.
1982
Nonholonomic problems and the theory of distributions. Zbl 0666.58004
Vershik, A. M.; Gershkovich, V. Ya.
1988
Statistical properties of locally free groups with applications to braid groups and growth of random heaps. Zbl 1010.20056
Vershik, A. M.; Nechaev, S.; Bikbov, R.
2000
Representations of the group $$\text{SL}(2, R)$$, where $$R$$ is a ring of functions. Zbl 0297.22003
Vershik, A. M.; Gel’fand, I. M.; Graev, M. I.
1973
Representations of the group of smooth mappings of a manifold $$X$$ into a compact Lie group. Zbl 0368.53034
Gelfand, I. M.; Graev, M. I.; Vershik, A. M.
1977
Geometry and dynamics of admissible metrics in measure spaces. Zbl 1261.37004
Vershik, Anatoly M.; Zatitskiy, Pavel B.; Petrov, Fedor V.
2013
Some characteristic properties of Gaussian stochastic processes. Zbl 0141.15203
Vershik, A. M.
1965
The theory of decreasing sequences of measurable partitions. Zbl 0853.28009
Vershik, A. M.
1994
The theorem about the periodic Markov approximation in ergodic theory. Zbl 0505.47006
Vershik, A. M.
1982
A new approach to the representation theory of symmetric groups. II. Zbl 1083.20502
Vershik, A. M.; Okoun’kov, A. Yu.
2005
The problem of describing central measures on the path spaces of graded graphs. Zbl 1370.37005
Vershik, A. M.
2014
Equipped graded graphs, projective limits of simplices, and their boundaries. Zbl 1323.05127
Vershik, A. M.
2015
The limit shape and fluctuations of random partitions of naturals with fixed number of summands. Zbl 0996.05006
Vershik, A.; Yakubovich, Yu.
2001
Polymorphisms, Markov processes, and quasi-similarity. Zbl 1115.37002
Vershik, A. M.
2005
Asymptotic combinatorics and algebraic analysis. Zbl 0843.05003
Vershik, Anatoly M.
1995
Continuum analogues of contragredient Lie algebras. (Lie algebras with a Cartan operator and nonlinear dynamical systems). Zbl 0691.17012
Savel’ev, M. V.; Vershik, A. M.
1989
Twisted Burnside theorem for type $$\text{II}_1$$ groups: an example. Zbl 1143.20026
Fel’shtyn, Alexander; Troitsky, Evgenij; Vershik, Anatoly
2006
Globalization of the partial isometries of metric spaces and local approximation of the group of isometries of Urysohn space. Zbl 1160.54020
Vershik, A. M.
2008
Bijective arithmetic codings of hyperbolic automorphisms of the $$2$$-torus, and binary quadratic forms. Zbl 0949.37023
Sidorov, N.; Vershik, A.
1998
Cohomology of groups in unitary representations, the neighborhood of the identity, and conditionally positive definite functions. Zbl 0528.43005
Vershik, A. M.; Karpushev, S. I.
1984
Dynamics of metrics in measure spaces and their asymptotic invariants. Zbl 1203.37020
Vershik, A. M.
2010
Intrinsic metric on graded graphs, standardness, and invariant measures. Zbl 1336.28014
Vershik, A. M.
2014
Irreducible representations of the group $$G^X$$ and cohomologies. Zbl 0299.22004
Vershik, A. M.; Gel’fand, I. M.; Graev, M. I.
1974
Fock factorizations and decompositions of the $$L^ 2$$ spaces over general Lévy processes. Zbl 1060.46056
Vershik, A. M.; Tsilevich, N. V.
2003
Quasi-invariance du processus gamma et propriétés multiplicatives des distributions de Poisson-Dirichlet. (Quasi-invariance of the gamma process and multiplicative properties of the Poisson-Dirichlet measures.) Zbl 0938.60040
Tsilevich, Natalia; Vershik, Anatoly
1999
Classification of measurable functions of several variables and invariantly distributed random matrices. Zbl 1025.28010
Vershik, A. M.
2002
Limit measures arising in the asymptotic theory of symmetric groups. II. Zbl 0423.60009
Vershik, A. M.; Shmidt, A. A.
1978
A local limit theorem for random strict partitions. Zbl 0969.60034
Vershik, A. M.; Freĭman, G. A.; Yakubovich, Yu. V.
1999
Arithmetic isomorphism of hyperbolic toral automorphisms and sofic shifts. Zbl 0810.58031
Vershik, A. M.
1992
Nonholonomic manifolds and nilpotent analysis. Zbl 0693.53006
Gershkovich, V.; Vershik, A.
1988
Finite traces and representations of the group of infinite matrices over a finite field. Zbl 1286.22004
Gorin, Vadim; Kerov, Sergei; Vershik, Anatoly
2014
Frobenius-Schur functions (with an appendix by Vladimir Ivanov). Zbl 1051.05077
Olshanski, Grigori; Regev, Amitai; Vershik, Anatoly
2003
On the Markov-Krein identity and quasi-invariance of the gamma process. Zbl 1069.60046
Vershik, A.; Yor, M.; Tsilevich, N.
2001
Some remarks on the infinite-dimensional problems of linear programming. Zbl 0224.90041
Vershik, A. M.
1970
Representations of the group of functions taking values in a compact Lie group. Zbl 0449.22019
Gelfand, I. M.; Graev, M. I.; Vershik, A. M.
1980
Limit distribution of the energy of a quantum ideal gas from the viewpoint of the theory of partitions of natural numbers. Zbl 0927.60089
Vershik, A. M.
1997
Random walks on braid groups: Brownian bridges, complexity and statistics. Zbl 0901.60010
Nechaev, S. K.; Grosberg, A. Yu.; Vershik, A. M.
1996
Theorem on lacunary isomorphisms of monotonic sequences of partitions. Zbl 0186.20203
Vershik, A. M.
1968
Probability measures in infinite-dimensional spaces. Zbl 0248.60007
Vershik, A. M.; Sudakov, V. N.
1969
Characters and realizations of representations of an infinite-dimensional Hecke algebra, and knot invariants. Zbl 0716.20008
Vershik, A. M.; Kerov, S. V.
1989
Local stationary algebras. Zbl 0810.16015
Vershik, A. M.
1991
Cohomology of groups in unitary representations, neighbourhood of the unit and conditionally positive definite functions. Zbl 0513.43009
Vershik, A. M.; Karpushev, S. I.
1982
Many-valued measure-preserving mappings (polymorphisms) and Markovian operators. Zbl 0517.28016
Vershik, A. M.
1983
A commutative model of presentation of the group of flows $$SL(2,R)^ X$$ that is connected with a unipotent subgroup. Zbl 0536.22008
Vershik, A. M.; Gel’fand, I. M.; Graev, M. I.
1983
The theory of filtrations of subalgebras, standardness, and independence. Zbl 1370.05220
Vershik, A. M.
2017
The Pascal automorphism has a continuous spectrum. Zbl 1271.37007
Vershik, A. M.
2011
Examples of nonlinear continuous tensor products of measure spaces and non-Fock factorizations. Zbl 0912.46022
Tsirelson, B. S.; Vershik, A. M.
1998
Product of commuting spectral measures need not be countably additive. Zbl 0423.28008
Birman, M. Sh.; Vershik, A. M.; Solomyak, M. Z.
1979
Structure of the complementary series and special representations of the groups $$O(n,1)$$ and $$U(n,1)$$. Zbl 1148.22017
Vershik, A. M.; Graev, M. I.
2006
$$C^*$$-algebras associated with endomorphisms and polymorphisms of compact abelian groups. Zbl 1278.46050
Cuntz, Joachim; Vershik, Anatoly
2013
Convex rearrangements of random walks. (Réarrangements convexes des marches aléatoires.) Zbl 0903.60006
Davydov, Yu.; Vershik, A. M.
1998
Ergodicity and totality of partitions associated with the RSK correspondence. Zbl 1475.05171
Vershik, A. M.; Tsilevich, N. V.
2021
A method of defining central and Gibbs measures and the ergodic method. Zbl 07424703
Vershik, A. M.
2021
Combinatorial encoding of Bernoulli schemes and the asymptotic behavior of Young tableaux. Zbl 1450.05098
Vershik, A. M.
2020
Three theorems on the uniqueness of the Plancherel measure from different viewpoints. Zbl 1436.20020
Vershik, A. M.
2019
Asymptotics of the partition of the cube into Weyl simplices and an encoding of a Bernoulli scheme. Zbl 1427.37033
Vershik, A. M.
2019
The absolute of finitely generated groups. I: Commutative (semi)groups. Zbl 1403.28014
Vershik, Anatoly M.; Malyutin, Andrei V.
2018
Infinite geodesics in the discrete Heisenberg group. Zbl 1393.37047
Vershik, A. M.; Malyutin, A. V.
2018
The absolute of finitely generated groups. II: The Laplacian and degenerate parts. Zbl 1483.20125
Vershik, A. M.; Malyutin, A. V.
2018
The theory of filtrations of subalgebras, standardness, and independence. Zbl 1370.05220
Vershik, A. M.
2017
On the relationship between combinatorial functions and representation theory. Zbl 1369.20013
Vershik, A. M.; Tsilevich, N. V.
2017
Special representations of the Iwasawa subgroups of simple Lie groups. Zbl 1375.22010
Vershik, A. M.; Graev, M. I.
2017
Universal adic approximation, invariant measures and scaled entropy. Zbl 1382.37009
Vershik, Anatolii M.; Zatitskii, Pavel B.
2017
Equivalence of the Brownian and energy representations. Zbl 1360.22026
Albeverio, S.; Driver, B. K.; Gordina, Maria; Vershik, A. M.
2016
Cohomology of the Iwasawa subgroup of the group $$U(p,p)$$ in nonunitary representations. Zbl 1354.22019
Vershik, A. M.; Graev, M. I.
2016
Integration of virtually continuous functions over bistochastic measures and the trace formula for nuclear operators. Zbl 1345.28001
Vershik, A. M.; Zatitskiĭ, P. B.; Petrov, F. V.
2016
Smoothness and standardness in the theory of $$AF$$-algebras and in the problem on invariant measures. Zbl 1388.22004
Vershik, A.
2016
Asymptotic theory of path spaces of graded graphs and its applications. Zbl 1409.37051
Vershik, Anatoly M.
2016
Equipped graded graphs, projective limits of simplices, and their boundaries. Zbl 1323.05127
Vershik, A. M.
2015
Laplace operators on the cone of Radon measures. Zbl 1327.60105
Kondratiev, Yuri; Lytvynov, Eugene; Vershik, Anatoly
2015
Classification of finite metric spaces and combinatorics of convex polytopes. Zbl 1348.54021
Vershik, A. M.
2015
Phase transition in the exit boundary problem for random walks on groups. Zbl 1328.60117
Vershik, A. M.; Malyutin, A. V.
2015
Several remarks on Pascal automorphism and infinite ergodic theory. Zbl 1344.37012
Vershik, Anatoly M.
2015
The serpentine representation of the infinite symmetric group and the basic representation of the affine Lie algebra $$\widehat{\mathfrak{sl}_2}$$. Zbl 1319.20011
Tsilevich, Natalia V.; Vershik, Anatoly M.
2015
Standardness as an invariant formulation of independence. Zbl 1383.28001
Vershik, A. M.
2015
The problem of describing central measures on the path spaces of graded graphs. Zbl 1370.37005
Vershik, A. M.
2014
Intrinsic metric on graded graphs, standardness, and invariant measures. Zbl 1336.28014
Vershik, A. M.
2014
Finite traces and representations of the group of infinite matrices over a finite field. Zbl 1286.22004
Gorin, Vadim; Kerov, Sergei; Vershik, Anatoly
2014
Infinite-dimensional Schur-Weyl duality and the Coxeter-Laplace operator. Zbl 1306.20007
Tsilevich, N. V.; Vershik, A. M.
2014
Cohomology in nonunitary representations of semisimple Lie groups (the group $$U(2,2)$$). Zbl 1317.22011
Vershik, A. M.; Graev, M. I.
2014
A few snapshots from the work of Mikhail Gromov. Zbl 1317.01017
Burago, D.; Eliashberg, Y.; Bestvina, M.; Forstnerič, F.; Guth, L.; Nabutovsky, A.; Phillips, A.; Roe, J.; Vershik, A.
2014
Virtual continuity of measurable functions and its applications. Zbl 1320.28003
Vershik, A. M.; Zatitskiy, P. B.; Petrov, F. V.
2014
Nonsingular transformations of symmetric Lévy processes. Zbl 1317.60057
Vershik, A. M.; Smorodina, N. V.
2014
Two ways to define compatible metrics on the simplex of measures. Zbl 1319.46024
Vershik, A. M.
2014
Long history of the Monge-Kantorovich transportation problem. Zbl 1284.01041
Vershik, A. M.
2013
Geometry and dynamics of admissible metrics in measure spaces. Zbl 1261.37004
Vershik, Anatoly M.; Zatitskiy, Pavel B.; Petrov, Fedor V.
2013
$$C^*$$-algebras associated with endomorphisms and polymorphisms of compact abelian groups. Zbl 1278.46050
Cuntz, Joachim; Vershik, Anatoly
2013
Virtual continuity of measurable functions of several variables and embedding theorems. Zbl 1305.28004
Vershik, A. M.; Zatitskiy, P. B.; Petrov, F. V.
2013
On classification of measurable functions of several variables. Zbl 1388.28003
Vershik, A. M.
2013
Special representations of nilpotent Lie groups and the associated Poisson representations of current groups. Zbl 1298.22006
Vershik, Anatoly M.; Graev, Mark I.
2013
Totally nonfree actions and the infinite symmetric group. Zbl 1294.37004
Vershik, A. M.
2012
Scaling entropy and automorphisms with pure point spectrum. Zbl 1251.37009
Vershik, A. M.
2012
The Poisson model of the Fock space and representations of current groups. Zbl 1256.81058
Vershik, A. M.; Graev, M. I.
2012
Special representations of the groups $$U(\infty,1)$$ and $$O(\infty,1)$$ and the associated representations of the current groups $$U(\infty,1)^X$$ and $$O(\infty,1)^X$$ in quasi-Poisson spaces. Zbl 1279.22032
Vershik, A. M.; Graev, M. I.
2012
Leonid Vital’evich Kantorovich (on the 100th anniversary of his birth). Zbl 1253.01043
Vershik, A. M.; Kutateladze, S. S.; Novikov, S. P.
2012
Nonfree actions of countable groups and their characters. Zbl 1279.37004
Vershik, A. M.
2011
The Pascal automorphism has a continuous spectrum. Zbl 1271.37007
Vershik, A. M.
2011
Description of the characters and factor representations of the infinite symmetric inverse semigroup. Zbl 1271.20072
Vershik, A. M.; Nikitin, P. P.
2011
The word and geodesic problems in free solvable groups. Zbl 1207.20026
Myasnikov, A.; Roman&rsquo;kov, V.; Ushakov, A.; Vershik, A.
2010
Dynamics of metrics in measure spaces and their asymptotic invariants. Zbl 1203.37020
Vershik, A. M.
2010
Uncountable graphs and invariant measures on the set of universal countable graphs. Zbl 1209.05158
Petrov, Fedor; Vershik, Anatoly
2010
Numerical experiments in problems of asymptotic representation theory.. Zbl 1288.20012
Vershik, A.; Pavlov, D.
2010
Orbit theory, locally finite permutations and Morse arithmetic. Zbl 1217.37002
Vershik, A. M.
2010
Mikhail Shlemovich Birman (obituary). Zbl 1219.01025
Babich, V. M.; Buslaev, V. S.; Vershik, A. M.; Gindikin, S. G.; Kislyakov, S. V.; Laptev, A.; Marchenko, V. A.; Nikol&rsquo;skii, N. K.; Pastur, L. A.; Plamenevskii, B. A.; Solomyak, M. Z.; Suslina, T. A.; Ural&rsquo;tseva, N. N.; Faddeev, L. D.; Khavin, V. P.; Yafaev, D. R.
2010
Integral models of representations of the current groups of simple Lie groups. Zbl 1202.22019
Vershik, A. M.; Graev, M. I.
2009
The adic realization of the Morse transformation and the extension of its action to the solenoid. Zbl 1303.37004
Vershik, A. M.; Solomyak, B.
2009
Linearly rigid metric spaces and the embedding problem. Zbl 1178.46016
Melleray, J.; Petrov, F. V.; Vershik, A. M.
2008
Globalization of the partial isometries of metric spaces and local approximation of the group of isometries of Urysohn space. Zbl 1160.54020
Vershik, A. M.
2008
Scaled entropy of filtrations of $$\sigma$$-fields. Zbl 1161.28005
Vershik, A. M.; Gorbulsky, A. D.
2008
Integral models of representations of current groups. Zbl 1162.22019
Vershik, A. M.; Graev, M. I.
2008
Algebraic polymorphisms. Zbl 1154.37304
Schmidt, Klaus; Vershik, Anatoly
2008
Invariant measures for the continual Cartan subgroup. Zbl 1187.37007
Vershik, A. M.
2008
The behavior of the Laplace transform of the invariant measure on the hypersphere of high dimension. Zbl 1178.58010
Vershik, A. M.
2008
A new approach to the representation theory of the symmetric groups. IV: $$\mathbb{Z}_2$$-graded groups and algebras; projective representations of the group $$S_n$$. Zbl 1196.20017
Vershik, A. M.; Sergeev, A. N.
2008
The local stationary presentation of the alternating groups and the normal form. Zbl 1150.20001
Vershik, A.; Vsemirnov, M.
2008
Integral models of unitary representations of current groups with values in semidirect products. Zbl 1162.22020
Vershik, A. M.; Graev, M. I.
2008
Representation theory, dynamical systems, combinatorial methods. Part 16. (Теория представлений, динамические системы, комбинаторные методы. 16.) Zbl 1170.49302
2008
Boundaries of braid groups and the Markov-Ivanovsky normal form. Zbl 1155.60033
Vershik, A. M.; Malyutin, A. V.
2008
Does there exist a Lebesgue measure in the infinite-dimensional space? Zbl 1165.28003
Vershik, A. M.
2007
Induced representations of the infinite symmetric group. Zbl 1153.20008
Tsilevich, N. V.; Vershik, A. M.
2007
Krein duality, positive 2-algebras, and the dilation of comultiplications. Zbl 1184.16034
Vershik, A. M.
2007
Induced representations of the infinite symmetric group and their spectral theory. Zbl 1327.20010
Vershik, A. M.; Tsilevich, N. V.
2007
Markov measures on Young tableaux and induced representations of the infinite symmetric group. Zbl 1155.20013
Vershik, A. M.; Tsilevich, N. V.
2007
Representation theory, dynamical systems, combinatorial methods. Part 15. Transl. from the Russian. Zbl 1136.49301
2007
What is good for mathematics? Thoughts on the Clay Millennium Prizes. Zbl 1128.01314
Vershik, Anatoly
2007
$$C^*$$-algebras of irreversible dynamical systems. Zbl 1104.46037
Exel, R.; Vershik, A.
2006
Some isometry groups of the Urysohn space. Zbl 1108.54027
Cameron, P. J.; Vershik, A. M.
2006
The Kantorovich metric: the initial history and little-known applications. Zbl 1090.28009
Vershik, A. M.
2006
Twisted Burnside theorem for type $$\text{II}_1$$ groups: an example. Zbl 1143.20026
Fel&rsquo;shtyn, Alexander; Troitsky, Evgenij; Vershik, Anatoly
2006
Structure of the complementary series and special representations of the groups $$O(n,1)$$ and $$U(n,1)$$. Zbl 1148.22017
Vershik, A. M.; Graev, M. I.
2006
On different models of representations of the infinite symmetric group. Zbl 1149.20013
Tsilevich, N. V.; Vershik, A. M.
2006
Fluctuations of the maximal particle energy of the quantum ideal gas and random partitions. Zbl 1113.82010
Vershik, A.; Yakubovich, Yu.
2006
What does a generic Markov operator look like? Zbl 1173.47306
Vershik, A. M.
2006
Gelfand-Tsetlin algebras, expectations, inverse limits, Fourier analysis. Zbl 1101.22002
Vershik, A. M.
2006
Traces on infinite-dimensional Brauer algebras. Zbl 1137.20011
Nikitin, P. P.; Vershik, A. M.
2006
Compactness of the congruence group of measurable functions in several variables. Zbl 1127.28001
Vershik, A. M.; Haböck, U.
2006
Universality and randomness for the graphs and metric spaces. 2nd printing. Zbl 1134.05098
Vershik, A. M.
2006
A new approach to the representation theory of symmetric groups. II. Zbl 1083.20502
Vershik, A. M.; Okoun&rsquo;kov, A. Yu.
2005
Polymorphisms, Markov processes, and quasi-similarity. Zbl 1115.37002
Vershik, A. M.
2005
The basic representation of the current group $$O(n,1)^X$$ in the $$L^2$$ space over the generalized Lebesgue measure. Zbl 1147.22013
Graev, M. I.; Vershik, A. M.
2005
Geometrical approach to the free solvable groups. Zbl 1104.20034
Vershik, A. M.; Dobrynin, S. V.
2005
A commutative model of a representation of the group $$O(n, 1)^{X}$$ and a generalized Lebesgue measure in the space of distributions. Zbl 1135.22018
Graev, M. I.; Vershik, A. M.
2005
On the Fourier transform on the infinite symmetric group. Zbl 1078.43002
Vershik, A. M.; Tsilevich, N. V.
2005
Harmonic analysis on the infinite symmetric group. Zbl 1057.43005
Kerov, Sergei; Olshanski, Grigori; Vershik, Anatoly
2004
Random and universal metric spaces. Zbl 1124.28012
Vershik, Anatoly M.
2004
Ol’ga Aleksandrovna Ladyzhenskaya (obituary). Zbl 1062.01503
Arnol&rsquo;d, V. I.; Birman, M. Sh.; Vershik, A. M.; et al.
2004
Random metric spaces and universality. Zbl 1065.60005
Vershik, A. M.
2003
Fock factorizations and decompositions of the $$L^ 2$$ spaces over general Lévy processes. Zbl 1060.46056
Vershik, A. M.; Tsilevich, N. V.
2003
Frobenius-Schur functions (with an appendix by Vladimir Ivanov). Zbl 1051.05077
Olshanski, Grigori; Regev, Amitai; Vershik, Anatoly
2003
Two lectures on the asymptotic representation theory and statistics of Young diagrams. Zbl 1035.05101
Vershik, A.
2003
Asymptotics of the uniform measure on simplices, and random compositions and partitions. Zbl 1081.60009
Vershik, A. M.; Yakubovich, Yu. V.
2003
...and 184 more Documents
all top 5

### Cited by 1,894 Authors

 113 Vershik, Anatoliĭ Moiseevich 41 Maslov, Viktor Pavlovich 31 Ol’shanskiĭ, Grigoriĭ Iosifovich 26 Borodin, Alexei 22 Kerov, Sergei V. 22 Neretin, Yuriĭ Aleksandrovich 18 Albeverio, Sergio A. 16 Kaimanovich, Vadim A. 16 Petrov, Fedor Vladimirovich 16 Sachkov, Yuriĭ Leonidovich 15 Tsilevich, Natalia V. 13 Gorin, Vadim 13 Graev, Mark Iosifovich 13 Lytvynov, Eugene W. 12 Bufetov, Aleksandr Igorevich 12 Bufetov, Alekseĭ Igor’evich 12 Erschler, Anna 12 Zatitskii, Pavel B. 11 Grigorchuk, Rostislav Ivanovich 11 Petrov, Leonid 10 Kondrat’yev, Yuriĭ Grygorovych 10 Nazaikinskii, Vladimir E. 10 Peres, Yuval 10 Sakbaev, Vsevolod Zhanovich 10 Solomyak, Boris 10 Woess, Wolfgang 9 Bogolyubov, Nikolaĭ Mikhaĭlovich 9 Fel’shtyn, Alexander 9 Pak, Igor 9 Ryzhikov, Valeriĭ Valentinovich 9 Śniady, Piotr 9 Troitskiĭ, Evgeniĭ Vadimovich 8 Berestovskiĭ, Valeriĭ Nikolaevich 8 Granovsky, Boris L. 8 Kabluchko, Zakhar A. 8 Okun’kov, Andreĭ Yur’evich 8 Panova, Greta 8 Rains, Eric M. 8 Sidorov, Nikita A. 8 Tamuz, Omer 7 Agrachev, Andreĭ Aleksandrovich 7 Bogachev, Leonid V. 7 Diaconis, Persi Warren 7 Feldman, Jacob 7 Hartman, Yair 7 Kirillov, Anatol N. 7 Melleray, Julien 7 Minabutdinov, A. R. 7 Myasnikov, Alexei G. 7 Regev, Amitai 7 Strahov, Eugene 7 Ushakov, Alexander S. 7 Yor, Marc 6 Berthé, Valérie 6 Björklund, Michael 6 Bowen, Lewis Phylip 6 Brieussel, Jérémie 6 Daletskii, Alexei 6 de León Rodríguez, Manuel 6 Dudko, Artem 6 Ferenczi, Sébastien 6 Fomin, Sergey Vladimirovich 6 Gnedin, Alexander V. 6 Grigoryan, Suren Arshakovich 6 Hołubowski, Waldemar 6 Hubička, Jan 6 Kapovich, Ilya 6 Mairesse, Jean 6 Nešetřil, Jaroslav 6 Schmidt, Klaus 6 Smorodina, Natal’ya Vasil’evna 6 Warnaar, S. Ole 6 Yakubovich, Yuri V. 5 Assiotis, Theodoros 5 Bárány, Imre 5 Bezuglyi, Sergey I. 5 Frenkel, Igor B. 5 Fulman, Jason E. 5 Goodman, Frederick M. 5 Høegh-Krohn, Raphael J. 5 Hora, Akihito 5 Kalantar, Mehrdad 5 Konečný, Matěj 5 Kosyak, Alexandre V. 5 Kuznetsova, Alla. Yu. 5 Kwaśniewski, Bartosz Kosma 5 Lijoi, Antonio 5 Malyutin, Andrei Valer’evich 5 Marsden, Jerrold Eldon 5 Mathéus, Frédéric 5 Molchanov, Vladimir Fedorovich 5 Najnudel, Joseph 5 Nessonov, Nikolai I. 5 Nikeghbali, Ashkan 5 Nikitin, Pavel P. 5 Petersen, Karl E. 5 Pitman, Jim William 5 Pittel, Boris G. 5 Raeburn, Iain 5 Ram, Arun ...and 1,794 more Authors
all top 5

### Cited in 349 Serials

 140 Journal of Mathematical Sciences (New York) 81 Functional Analysis and its Applications 62 Advances in Mathematics 58 Journal of Functional Analysis 54 The Annals of Probability 44 Transactions of the American Mathematical Society 43 Journal of Algebra 42 Mathematical Notes 40 Israel Journal of Mathematics 34 Journal of Soviet Mathematics 32 Siberian Mathematical Journal 31 Probability Theory and Related Fields 30 Journal of Mathematical Physics 30 Ergodic Theory and Dynamical Systems 29 Communications in Mathematical Physics 25 Proceedings of the American Mathematical Society 22 Advances in Applied Mathematics 22 Russian Journal of Mathematical Physics 19 Journal of Geometry and Physics 19 Annales de l’Institut Fourier 18 Duke Mathematical Journal 18 Topology and its Applications 18 Journal of Dynamical and Control Systems 17 Theoretical and Mathematical Physics 17 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 16 Journal of Statistical Physics 16 Journal of Algebraic Combinatorics 15 Inventiones Mathematicae 14 Journal of Combinatorial Theory. Series A 14 Monatshefte für Mathematik 14 Stochastic Processes and their Applications 13 Discrete Mathematics 12 Journal d’Analyse Mathématique 12 European Journal of Combinatorics 12 Discrete & Computational Geometry 12 International Journal of Algebra and Computation 11 Journal of Mathematical Analysis and Applications 11 Letters in Mathematical Physics 11 Journal of Theoretical Probability 11 The Annals of Applied Probability 11 Russian Mathematics 11 Infinite Dimensional Analysis, Quantum Probability and Related Topics 10 Journal of Differential Equations 10 Mathematische Zeitschrift 10 Acta Applicandae Mathematicae 10 Geometric and Functional Analysis. GAFA 10 Linear Algebra and its Applications 10 Bulletin of the American Mathematical Society. New Series 10 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 10 Proceedings of the Steklov Institute of Mathematics 10 Groups, Geometry, and Dynamics 9 Reports on Mathematical Physics 9 Russian Mathematical Surveys 9 Compositio Mathematica 9 Random Structures & Algorithms 9 St. Petersburg Mathematical Journal 9 Bernoulli 9 Doklady Mathematics 9 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 8 Communications in Algebra 8 Algebras and Representation Theory 7 Geometriae Dedicata 7 Mathematische Annalen 7 International Journal of Mathematics 7 Selecta Mathematica. New Series 7 Electronic Journal of Probability 7 Discrete and Continuous Dynamical Systems 7 Annals of Mathematics. Second Series 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 International Journal of Theoretical Physics 6 Theoretical Computer Science 6 Statistics & Probability Letters 6 Vestnik St. Petersburg University. Mathematics 5 Nuclear Physics. B 5 Reviews in Mathematical Physics 5 The Mathematical Intelligencer 5 Integral Equations and Operator Theory 5 Memoirs of the American Mathematical Society 5 Annals of Pure and Applied Logic 5 Differential Geometry and its Applications 5 Indagationes Mathematicae. New Series 5 SIAM Journal on Optimization 5 Combinatorics, Probability and Computing 5 The Electronic Journal of Combinatorics 4 Advances in Applied Probability 4 Nonlinearity 4 Theory of Probability and its Applications 4 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 4 Journal of Number Theory 4 Nagoya Mathematical Journal 4 Publications of the Research Institute for Mathematical Sciences, Kyoto University 4 Systems & Control Letters 4 Journal of the American Mathematical Society 4 Annales Mathématiques Blaise Pascal 4 Sbornik: Mathematics 4 Transformation Groups 4 Representation Theory 4 Annals of Combinatorics 4 Journal of High Energy Physics 4 Dynamical Systems ...and 249 more Serials
all top 5

### Cited in 60 Fields

 633 Probability theory and stochastic processes (60-XX) 402 Group theory and generalizations (20-XX) 391 Combinatorics (05-XX) 361 Dynamical systems and ergodic theory (37-XX) 233 Topological groups, Lie groups (22-XX) 196 Measure and integration (28-XX) 182 Functional analysis (46-XX) 137 Statistical mechanics, structure of matter (82-XX) 131 Abstract harmonic analysis (43-XX) 127 Differential geometry (53-XX) 108 Number theory (11-XX) 94 Global analysis, analysis on manifolds (58-XX) 92 Quantum theory (81-XX) 76 Operator theory (47-XX) 73 Convex and discrete geometry (52-XX) 69 Computer science (68-XX) 68 General topology (54-XX) 60 Nonassociative rings and algebras (17-XX) 56 Mechanics of particles and systems (70-XX) 54 Partial differential equations (35-XX) 51 Statistics (62-XX) 47 Associative rings and algebras (16-XX) 47 Special functions (33-XX) 46 Calculus of variations and optimal control; optimization (49-XX) 41 Mathematical logic and foundations (03-XX) 41 Linear and multilinear algebra; matrix theory (15-XX) 39 Manifolds and cell complexes (57-XX) 29 Operations research, mathematical programming (90-XX) 26 Systems theory; control (93-XX) 25 Numerical analysis (65-XX) 24 Information and communication theory, circuits (94-XX) 21 Algebraic geometry (14-XX) 20 Potential theory (31-XX) 18 History and biography (01-XX) 18 Order, lattices, ordered algebraic structures (06-XX) 18 Geometry (51-XX) 17 Fluid mechanics (76-XX) 16 Functions of a complex variable (30-XX) 16 Harmonic analysis on Euclidean spaces (42-XX) 15 Algebraic topology (55-XX) 14 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 11 Several complex variables and analytic spaces (32-XX) 11 Ordinary differential equations (34-XX) 10 Biology and other natural sciences (92-XX) 9 Category theory; homological algebra (18-XX) 9 Approximations and expansions (41-XX) 8 General and overarching topics; collections (00-XX) 7 Commutative algebra (13-XX) 7 Integral equations (45-XX) 6 Real functions (26-XX) 6 Difference and functional equations (39-XX) 6 Classical thermodynamics, heat transfer (80-XX) 6 Relativity and gravitational theory (83-XX) 5 $$K$$-theory (19-XX) 5 Integral transforms, operational calculus (44-XX) 3 General algebraic systems (08-XX) 3 Sequences, series, summability (40-XX) 2 Optics, electromagnetic theory (78-XX) 2 Mathematics education (97-XX) 1 Mechanics of deformable solids (74-XX)

### Wikidata Timeline

The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.