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Aizenman, Michael

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 Author ID: aizenman.michael Published as: Aizenman, M.; Aizenman, Michael Homepage: https://www.princeton.edu/~aizenman/ External Links: MGP · Math-Net.Ru · Wikidata · dblp · GND
 Documents Indexed: 83 Publications since 1975, including 2 Books Biographic References: 2 Publications
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Co-Authors

 16 single-authored 20 Warzel, Simone 8 Lebowitz, Joel Louis 6 Newman, Charles Michael 5 Schenker, Jeffrey H. 5 Sims, Robert L. 4 Goldstein, Sheldon 3 Duminil-Copin, Hugo 3 Lieb, Elliott H. 3 Peled, Ron 2 Barsky, David J. 2 Burchard, Almut 2 Chayes, Jennifer Tour 2 Chayes, Lincoln 2 Elgart, Alexander 2 Fernández, Roberto 2 Fröhlich, Jürg Martin 2 Jung, Paul H. 2 Kesten, Harry 2 Naboko, Serguei N. 2 Seiringer, Robert 2 Shamis, Mira 2 Solovej, Jan Philip 2 Stolz, Gunter 2 Wehr, Jan 2 Yngvason, Jakob 1 Araki, Huzihiro 1 Arguin, Louis-Pierre 1 Bak, Thor A. 1 Bricmont, Jean 1 Contucci, Pierluigi 1 Corwin, Ivan 1 Davies, Edward Brian 1 Friedrich, Roland M. 1 Gallavotti, Giovanni M. 1 Germinet, François 1 Goldstein, Shelly 1 Graf, Gian Michele 1 Greenblatt, Rafael Leon 1 Harel, Matan 1 Holley, Richard A. 1 Hundertmark, Dirk 1 Jansen, Sabine 1 Klein, Abel 1 Molchanov, Stanislav Alekseevich 1 Nachtergaele, Bruno 1 Ruelle, David Pierre 1 Russo, Lucio 1 Ruzmaikina, Anastasia A. 1 Sidoravicius, Vladas 1 Simon, Barry 1 Sodin, Sasha 1 Spohn, Herbert 1 Starr, Shannon L. 1 Tassion, Vincent 1 Valcázar, Manuel Laínz 1 Wilson, David Bruce
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Serials

 18 Communications in Mathematical Physics 12 Journal of Statistical Physics 3 The Annals of Probability 3 Probability Theory and Related Fields 3 Annales Henri Poincaré 2 Communications on Pure and Applied Mathematics 2 Journal of Mathematical Physics 2 Letters in Mathematical Physics 2 Duke Mathematical Journal 2 Inventiones Mathematicae 2 Journal of Physics A: Mathematical and General 1 Nuclear Physics. B 1 Physica A 1 Reviews in Mathematical Physics 1 Advances in Mathematics 1 Random Structures & Algorithms 1 Mathematical Physics, Analysis and Geometry 1 Annals of Mathematics. Second Series 1 Journal of the European Mathematical Society (JEMS) 1 Communications in Contemporary Mathematics 1 Nieuw Archief voor Wiskunde. Vijfde Serie 1 Moscow Mathematical Journal 1 Advanced Series in Mathematical Physics 1 Graduate Studies in Mathematics 1 ALEA. Latin American Journal of Probability and Mathematical Statistics 1 Journal of Physics A: Mathematical and Theoretical
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Fields

 60 Statistical mechanics, structure of matter (82-XX) 41 Probability theory and stochastic processes (60-XX) 17 Quantum theory (81-XX) 16 Operator theory (47-XX) 6 Partial differential equations (35-XX) 5 Combinatorics (05-XX) 5 Measure and integration (28-XX) 4 Ordinary differential equations (34-XX) 4 Dynamical systems and ergodic theory (37-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Fluid mechanics (76-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Difference and functional equations (39-XX) 1 Functional analysis (46-XX) 1 General topology (54-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX)

Citations contained in zbMATH

72 Publications have been cited 2,434 times in 1,610 Documents Cited by Year
Localization at large disorder and at extreme energies: an elementary derivation. Zbl 0782.60044
Aizenman, Michael; Molchanov, Stanislav
1993
Brownian motion and Harnack inequality for Schrödinger operators. Zbl 0459.60069
Aizenman, M.; Simon, B.
1982
Discontinuity of the magnetization in one-dimensional $$1/| x-y| ^ 2$$ Ising and Potts models. Zbl 1084.82514
Aizenman, M.; Chayes, J. T.; Chayes, L.; Newman, C. M.
1988
Sharpness of the phase transition in percolation models. Zbl 0618.60098
Aizenman, Michael; Barsky, David J.
1987
Geometric analysis of $$\phi^ 4$$ fields and Ising models. I, II. Zbl 0533.58034
Aizenman, Michael
1982
Localization at weak disorder: some elementary bounds. Zbl 0843.47039
Aizenman, Michael
1994
Metastability effects in bootstrap percolation. Zbl 0656.60106
Aizenman, M.; Lebowitz, J. L.
1988
Tree graph inequalities and critical behavior in percolation models. Zbl 0586.60096
Aizenman, Michael; Newman, Charles M.
1984
Finite-volume fractional-moment criteria for Anderson localization. Zbl 1038.82038
Aizenman, Michael; Schenker, Jeffrey H.; Friedrich, Roland M.; Hundertmark, Dirk
2001
Rounding effects of quenched randomness on first-order phase transitions. Zbl 0714.60090
Aizenman, Michael; Wehr, Jan
1990
Some rigorous results on the Sherrington-Kirkpatrick spin glass model. Zbl 1108.82312
Aizenman, M.; Lebowitz, J. L.; Ruelle, D.
1987
Random operators. Disorder effects on quantum spectra and dynamics. Zbl 1333.82001
Aizenman, Michael; Warzel, Simone
2015
Convergence to equilibrium in a system of reacting polymers. Zbl 0458.76062
Aizenman, Michael; Bak, Thor A.
1979
On the stability of the quenched state in mean-field spin-glass models. Zbl 0963.82045
Aizenman, M.; Contucci, P.
1998
Moment analysis for localization in random Schrödinger operators. Zbl 1090.81026
Aizenman, Michael; Elgart, Alexander; Naboko, Serguei; Schenker, Jeffrey H.; Stolz, Gunter
2006
Uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolation. Zbl 0642.60102
Aizenman, M.; Kesten, H.; Newman, C. M.
1987
Discontinuity of the percolation density in one dimensional $$1/| x- y| ^ 2$$ percolation models. Zbl 0613.60097
Aizenman, M.; Newman, C. M.
1986
Localization bounds for an electron gas. Zbl 0953.82009
Aizenman, M.; Graf, G. M.
1998
On the critical behavior of the magnetization in high-dimensional Ising models. Zbl 0629.60106
Aizenman, M.; Fernández, R.
1986
Hölder regularity and dimension bounds for random curves. Zbl 0944.60022
Aizenman, M.; Burchard, A.
1999
Stability of the absolutely continuous spectrum of random Schrödinger operators on tree graphs. Zbl 1169.82007
Aizenman, Michael; Sims, Robert; Warzel, Simone
2006
Geometric aspects of quantum spin states. Zbl 0799.58087
Aizenman, Michael; Nachtergaele, Bruno
1994
On a sharp transition from area law to perimeter law in a system of random surfaces. Zbl 0529.60099
Aizenman, M.; Chayes, J. T.; Chayes, L.; Fröhlich, J.; Russo, L.
1983
Localization bounds for multiparticle systems. Zbl 1186.82055
Aizenman, Michael; Warzel, Simone
2009
Percolation critical exponents under the triangle condition. Zbl 0747.60093
Barsky, D. J.; Aizenman, M.
1991
On the structure of quasi-stationary competing particle systems. Zbl 1177.60050
Arguin, Louis-Pierre; Aizenman, Michael
2009
Random currents and continuity of Ising model’s spontaneous magnetization. Zbl 1315.82004
Aizenman, Michael; Duminil-Copin, Hugo; Sidoravicius, Vladas
2015
Resonant delocalization for random Schrödinger operators on tree graphs. Zbl 1267.47064
Aizenman, Michael; Warzel, Simone
2013
Characterization of invariant measures at the leading edge for competing particle systems. Zbl 1096.60042
Ruzmaikina, Anastasia; Aizenman, Michael
2005
Absolutely continuous spectra of quantum tree graphs with weak disorder. Zbl 1233.34009
Aizenman, Michael; Sims, Robert; Warzel, Simone
2006
On the number of incipient spanning clusters. Zbl 0925.82112
Aizenman, Michael
1997
Rapid convergence to equilibrium of stochastic Ising models in the Dobrushin Shlosman regime. Zbl 0621.60118
Aizenman, M.; Holley, R.
1987
The Canophy graph and level statistics for random operators on trees. Zbl 1138.47032
Aizenman, Michael; Warzel, Simone
2006
Fluctuations of extensive functions of quenched random couplings. Zbl 0718.60129
Wehr, Jan; Aizenman, Michael
1990
On vector fields as generators of flows: A counterexample to Nelson’s conjecture. Zbl 0394.28012
Aizenman, Michael
1978
The intersection of Brownian paths as a case study of a renormalization group method for quantum field theory. Zbl 0573.60076
Aizenman, Michael
1985
The creation of spectral gaps by graph decoration. Zbl 0990.47006
Schenker, Jeffrey H.; Aizenman, Michael
2000
Bose-Einstein condensation as a quantum phase transition in an optical lattice. Zbl 1170.82325
Aizenman, M.; Lieb, E. H.; Seiringer, R.; Solovej, J. P.; Yngvason, J.
2006
Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs. Zbl 1278.81090
Aizenman, Michael; Warzel, Simone
2012
Scaling limits for minimal and random spanning trees in two dimensions. Zbl 0939.60031
Aizenman, Michael; Burchard, Almut; Newman, Charles M.; Wilson, David B.
1999
On Bernoulli decompositions for random variables, concentration bounds, and spectral localization. Zbl 1152.60020
Aizenman, Michael; Germinet, François; Klein, Abel; Warzel, Simone
2009
Mean-field spin glass models from the cavity-ROSt perspective. Zbl 1175.82033
Aizenman, Michael; Sims, Robert; Starr, Shannon L.
2007
Critical exponents for long-range interactions. Zbl 0658.60136
Aizenman, Michael; Fernández, Roberto
1988
Conditional equilibrium and the equivalence of microcanonical and grandcanonical ensembles in the thermodynamic limit. Zbl 0391.60097
Aizenman, Michael; Goldstein, Sheldon; Lebowitz, Joel L.
1978
Scaling limit for the incipient spanning clusters. Zbl 0941.74013
Aizenman, Michael
1998
On the slow decay of $$O(2)$$ correlations in the absence of topological excitations: Remark on the Patrascioiu-Seiler model. Zbl 0838.60096
Aizenman, Michael
1994
Precolation of the minority spins in high-dimensional Ising models. Zbl 0960.82503
Aizenman, M.; Bricmont, J.; Lebowitz, J. L.
1987
Bounded fluctuations and translation symmetry breaking in one-dimensional particle systems. Zbl 0999.82030
Aizenman, M.; Goldstein, S.; Lebowitz, J. L.
2001
A sufficient condition for the avoidance of sets by measure preserving flows in $$\mathbb R^ n$$. Zbl 0471.28015
Aizenman, Michael
1978
Ergodic properties of an infinite one dimensional hard rod system. Zbl 0352.60073
Aizenman, Michael; Goldstein, Sheldon; Lebowitz, Joel L.
1975
On the ubiquity of the Cauchy distribution in spectral problems. Zbl 1330.60042
Aizenman, Michael; Warzel, Simone
2015
Resonances and partial delocalization on the complete graph. Zbl 1329.81192
Aizenman, Michael; Shamis, Mira; Warzel, Simone
2015
Proof of rounding by quenched disorder of first order transitions in low-dimensional quantum systems. Zbl 1290.82014
Aizenman, Michael; Greenblatt, Rafael L.; Lebowitz, Joel L.
2012
On the critical behavior at the lower phase transition of the contact process. Zbl 1160.60332
Aizenman, Michael; Jung, Paul
2007
Fluctuation-based proof of the stability of ac spectra of random operators on tree graphs. Zbl 1111.82022
Aizenman, Michael; Sims, Robert; Warzel, Simone
2006
Ergodic properties of infinite systems. Zbl 0316.28008
Goldstein, Sheldon; Lebowitz, Joel L.; Aizenman, Michael
1975
On the joint distribution of energy levels of random Schrödinger operators. Zbl 1156.47037
Aizenman, Michael; Warzel, Simone
2009
Emergent planarity in two-dimensional Ising models with finite-range interactions. Zbl 1417.82022
Aizenman, Michael; Duminil-Copin, Hugo; Tassion, Vincent; Warzel, Simone
2019
Symmetry breaking in quasi-1D Coulomb systems. Zbl 1209.82025
Aizenman, Michael; Jansen, Sabine; Jung, Paul
2010
Complete dynamical localization in disordered quantum multi-particle systems. Zbl 1205.82089
Aizenman, Michael; Warzel, Simone
2010
Exponential decay of correlations in the $$2D$$ random field Ising model. Zbl 07239465
Aizenman, Michael; Harel, Matan; Peled, Ron
2020
Persistence under weak disorder of AC spectra of quasi-periodic Schrödinger operators on trees graphs. Zbl 1124.47027
Aizenman, M.; Warzel, S.
2005
Rigorous studies of critical behavior. II. Zbl 0662.60114
Aizenman, Michael
1985
Positive linear maps which are order bounded on $$C^*$$ subalgebras. Zbl 0397.46058
Aizenman, Michael; Davies, E. Brian; Lieb, Elliott H.
1978
A power-law upper bound on the correlations in the 2D random field Ising model. Zbl 1447.82005
Aizenman, Michael; Peled, Ron
2019
Kac-Ward formula and its extension to order-disorder correlators through a graph zeta function. Zbl 1405.82006
Aizenman, Michael; Warzel, Simone
2018
Pfaffian correlation functions of planar dimer covers. Zbl 1360.82016
Aizenman, Michael; Valcázar, Manuel Laínz; Warzel, Simone
2017
Matrix regularizing effects of Gaussian perturbations. Zbl 1360.60012
Aizenman, Michael; Peled, Ron; Schenker, Jeffrey; Shamis, Mira; Sodin, Sasha
2017
Boosted Simon-Wolff spectral criterion and resonant delocalization. Zbl 1387.47025
Aizenman, Michael; Warzel, Simone
2016
General results in percolation theory. Zbl 0639.60099
Aizenman, Michael
1987
Rigorous studies of critical behavior. Zbl 0667.60102
Aizenman, Michael
1986
Stochastic geometry in statistical mechanics and quantum field theory. Zbl 0564.60012
Aizenman, Michael
1984
Exponential decay of correlations in the $$2D$$ random field Ising model. Zbl 07239465
Aizenman, Michael; Harel, Matan; Peled, Ron
2020
Emergent planarity in two-dimensional Ising models with finite-range interactions. Zbl 1417.82022
Aizenman, Michael; Duminil-Copin, Hugo; Tassion, Vincent; Warzel, Simone
2019
A power-law upper bound on the correlations in the 2D random field Ising model. Zbl 1447.82005
Aizenman, Michael; Peled, Ron
2019
Kac-Ward formula and its extension to order-disorder correlators through a graph zeta function. Zbl 1405.82006
Aizenman, Michael; Warzel, Simone
2018
Pfaffian correlation functions of planar dimer covers. Zbl 1360.82016
Aizenman, Michael; Valcázar, Manuel Laínz; Warzel, Simone
2017
Matrix regularizing effects of Gaussian perturbations. Zbl 1360.60012
Aizenman, Michael; Peled, Ron; Schenker, Jeffrey; Shamis, Mira; Sodin, Sasha
2017
Boosted Simon-Wolff spectral criterion and resonant delocalization. Zbl 1387.47025
Aizenman, Michael; Warzel, Simone
2016
Random operators. Disorder effects on quantum spectra and dynamics. Zbl 1333.82001
Aizenman, Michael; Warzel, Simone
2015
Random currents and continuity of Ising model’s spontaneous magnetization. Zbl 1315.82004
Aizenman, Michael; Duminil-Copin, Hugo; Sidoravicius, Vladas
2015
On the ubiquity of the Cauchy distribution in spectral problems. Zbl 1330.60042
Aizenman, Michael; Warzel, Simone
2015
Resonances and partial delocalization on the complete graph. Zbl 1329.81192
Aizenman, Michael; Shamis, Mira; Warzel, Simone
2015
Resonant delocalization for random Schrödinger operators on tree graphs. Zbl 1267.47064
Aizenman, Michael; Warzel, Simone
2013
Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs. Zbl 1278.81090
Aizenman, Michael; Warzel, Simone
2012
Proof of rounding by quenched disorder of first order transitions in low-dimensional quantum systems. Zbl 1290.82014
Aizenman, Michael; Greenblatt, Rafael L.; Lebowitz, Joel L.
2012
Symmetry breaking in quasi-1D Coulomb systems. Zbl 1209.82025
Aizenman, Michael; Jansen, Sabine; Jung, Paul
2010
Complete dynamical localization in disordered quantum multi-particle systems. Zbl 1205.82089
Aizenman, Michael; Warzel, Simone
2010
Localization bounds for multiparticle systems. Zbl 1186.82055
Aizenman, Michael; Warzel, Simone
2009
On the structure of quasi-stationary competing particle systems. Zbl 1177.60050
Arguin, Louis-Pierre; Aizenman, Michael
2009
On Bernoulli decompositions for random variables, concentration bounds, and spectral localization. Zbl 1152.60020
Aizenman, Michael; Germinet, François; Klein, Abel; Warzel, Simone
2009
On the joint distribution of energy levels of random Schrödinger operators. Zbl 1156.47037
Aizenman, Michael; Warzel, Simone
2009
Mean-field spin glass models from the cavity-ROSt perspective. Zbl 1175.82033
Aizenman, Michael; Sims, Robert; Starr, Shannon L.
2007
On the critical behavior at the lower phase transition of the contact process. Zbl 1160.60332
Aizenman, Michael; Jung, Paul
2007
Moment analysis for localization in random Schrödinger operators. Zbl 1090.81026
Aizenman, Michael; Elgart, Alexander; Naboko, Serguei; Schenker, Jeffrey H.; Stolz, Gunter
2006
Stability of the absolutely continuous spectrum of random Schrödinger operators on tree graphs. Zbl 1169.82007
Aizenman, Michael; Sims, Robert; Warzel, Simone
2006
Absolutely continuous spectra of quantum tree graphs with weak disorder. Zbl 1233.34009
Aizenman, Michael; Sims, Robert; Warzel, Simone
2006
The Canophy graph and level statistics for random operators on trees. Zbl 1138.47032
Aizenman, Michael; Warzel, Simone
2006
Bose-Einstein condensation as a quantum phase transition in an optical lattice. Zbl 1170.82325
Aizenman, M.; Lieb, E. H.; Seiringer, R.; Solovej, J. P.; Yngvason, J.
2006
Fluctuation-based proof of the stability of ac spectra of random operators on tree graphs. Zbl 1111.82022
Aizenman, Michael; Sims, Robert; Warzel, Simone
2006
Characterization of invariant measures at the leading edge for competing particle systems. Zbl 1096.60042
Ruzmaikina, Anastasia; Aizenman, Michael
2005
Persistence under weak disorder of AC spectra of quasi-periodic Schrödinger operators on trees graphs. Zbl 1124.47027
Aizenman, M.; Warzel, S.
2005
Finite-volume fractional-moment criteria for Anderson localization. Zbl 1038.82038
Aizenman, Michael; Schenker, Jeffrey H.; Friedrich, Roland M.; Hundertmark, Dirk
2001
Bounded fluctuations and translation symmetry breaking in one-dimensional particle systems. Zbl 0999.82030
Aizenman, M.; Goldstein, S.; Lebowitz, J. L.
2001
The creation of spectral gaps by graph decoration. Zbl 0990.47006
Schenker, Jeffrey H.; Aizenman, Michael
2000
Hölder regularity and dimension bounds for random curves. Zbl 0944.60022
Aizenman, M.; Burchard, A.
1999
Scaling limits for minimal and random spanning trees in two dimensions. Zbl 0939.60031
Aizenman, Michael; Burchard, Almut; Newman, Charles M.; Wilson, David B.
1999
On the stability of the quenched state in mean-field spin-glass models. Zbl 0963.82045
Aizenman, M.; Contucci, P.
1998
Localization bounds for an electron gas. Zbl 0953.82009
Aizenman, M.; Graf, G. M.
1998
Scaling limit for the incipient spanning clusters. Zbl 0941.74013
Aizenman, Michael
1998
On the number of incipient spanning clusters. Zbl 0925.82112
Aizenman, Michael
1997
Localization at weak disorder: some elementary bounds. Zbl 0843.47039
Aizenman, Michael
1994
Geometric aspects of quantum spin states. Zbl 0799.58087
Aizenman, Michael; Nachtergaele, Bruno
1994
On the slow decay of $$O(2)$$ correlations in the absence of topological excitations: Remark on the Patrascioiu-Seiler model. Zbl 0838.60096
Aizenman, Michael
1994
Localization at large disorder and at extreme energies: an elementary derivation. Zbl 0782.60044
Aizenman, Michael; Molchanov, Stanislav
1993
Percolation critical exponents under the triangle condition. Zbl 0747.60093
Barsky, D. J.; Aizenman, M.
1991
Rounding effects of quenched randomness on first-order phase transitions. Zbl 0714.60090
Aizenman, Michael; Wehr, Jan
1990
Fluctuations of extensive functions of quenched random couplings. Zbl 0718.60129
Wehr, Jan; Aizenman, Michael
1990
Discontinuity of the magnetization in one-dimensional $$1/| x-y| ^ 2$$ Ising and Potts models. Zbl 1084.82514
Aizenman, M.; Chayes, J. T.; Chayes, L.; Newman, C. M.
1988
Metastability effects in bootstrap percolation. Zbl 0656.60106
Aizenman, M.; Lebowitz, J. L.
1988
Critical exponents for long-range interactions. Zbl 0658.60136
Aizenman, Michael; Fernández, Roberto
1988
Sharpness of the phase transition in percolation models. Zbl 0618.60098
Aizenman, Michael; Barsky, David J.
1987
Some rigorous results on the Sherrington-Kirkpatrick spin glass model. Zbl 1108.82312
Aizenman, M.; Lebowitz, J. L.; Ruelle, D.
1987
Uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolation. Zbl 0642.60102
Aizenman, M.; Kesten, H.; Newman, C. M.
1987
Rapid convergence to equilibrium of stochastic Ising models in the Dobrushin Shlosman regime. Zbl 0621.60118
Aizenman, M.; Holley, R.
1987
Precolation of the minority spins in high-dimensional Ising models. Zbl 0960.82503
Aizenman, M.; Bricmont, J.; Lebowitz, J. L.
1987
General results in percolation theory. Zbl 0639.60099
Aizenman, Michael
1987
Discontinuity of the percolation density in one dimensional $$1/| x- y| ^ 2$$ percolation models. Zbl 0613.60097
Aizenman, M.; Newman, C. M.
1986
On the critical behavior of the magnetization in high-dimensional Ising models. Zbl 0629.60106
Aizenman, M.; Fernández, R.
1986
Rigorous studies of critical behavior. Zbl 0667.60102
Aizenman, Michael
1986
The intersection of Brownian paths as a case study of a renormalization group method for quantum field theory. Zbl 0573.60076
Aizenman, Michael
1985
Rigorous studies of critical behavior. II. Zbl 0662.60114
Aizenman, Michael
1985
Tree graph inequalities and critical behavior in percolation models. Zbl 0586.60096
Aizenman, Michael; Newman, Charles M.
1984
Stochastic geometry in statistical mechanics and quantum field theory. Zbl 0564.60012
Aizenman, Michael
1984
On a sharp transition from area law to perimeter law in a system of random surfaces. Zbl 0529.60099
Aizenman, M.; Chayes, J. T.; Chayes, L.; Fröhlich, J.; Russo, L.
1983
Brownian motion and Harnack inequality for Schrödinger operators. Zbl 0459.60069
Aizenman, M.; Simon, B.
1982
Geometric analysis of $$\phi^ 4$$ fields and Ising models. I, II. Zbl 0533.58034
Aizenman, Michael
1982
Convergence to equilibrium in a system of reacting polymers. Zbl 0458.76062
Aizenman, Michael; Bak, Thor A.
1979
On vector fields as generators of flows: A counterexample to Nelson’s conjecture. Zbl 0394.28012
Aizenman, Michael
1978
Conditional equilibrium and the equivalence of microcanonical and grandcanonical ensembles in the thermodynamic limit. Zbl 0391.60097
Aizenman, Michael; Goldstein, Sheldon; Lebowitz, Joel L.
1978
A sufficient condition for the avoidance of sets by measure preserving flows in $$\mathbb R^ n$$. Zbl 0471.28015
Aizenman, Michael
1978
Positive linear maps which are order bounded on $$C^*$$ subalgebras. Zbl 0397.46058
Aizenman, Michael; Davies, E. Brian; Lieb, Elliott H.
1978
Ergodic properties of an infinite one dimensional hard rod system. Zbl 0352.60073
Aizenman, Michael; Goldstein, Sheldon; Lebowitz, Joel L.
1975
Ergodic properties of infinite systems. Zbl 0316.28008
Goldstein, Sheldon; Lebowitz, Joel L.; Aizenman, Michael
1975
all top 5

Cited by 1,510 Authors

 39 Aizenman, Michael 28 Klein, Abel 28 Newman, Charles Michael 24 Warzel, Simone 23 Chayes, Lincoln 23 Duminil-Copin, Hugo 17 Barra, Adriano 17 Chayes, Jennifer Tour 17 Chulaevsky, Victor 17 Slade, Gordon 17 Stolz, Gunter 17 van der Hofstad, Remco W. 16 Bollobás, Béla 16 Elgart, Alexander 16 Germinet, François 15 Camia, Federico 15 van Enter, Aernout C. D. 14 Grimmett, Geoffrey R. 14 Panchenko, Dmitry 14 Schenker, Jeffrey H. 13 Arguin, Louis-Pierre 13 Nachtergaele, Bruno 13 Veselić, Ivan 12 Biskup, Marek 12 Chatterjee, Sourav 12 Contucci, Pierluigi 12 Ioffe, Dmitry 12 Klopp, Frédéric 11 Björnberg, Jakob Erik 11 Kozma, Gady 11 Lebowitz, Joel Louis 11 Simon, Barry 11 Sims, Robert L. 11 Ueltschi, Daniel 10 Crawford, Nicholas 10 Fröhlich, Jürg Martin 10 Hislop, Peter D. 10 Morris, Robert D. 10 Sakai, Akira 10 Sidoravicius, Vladas 9 Cassandro, Marzio 9 Damanik, David 9 Gravner, Janko 9 Hara, Takashi 9 Hutchcroft, Tom 9 Jitomirskaya, Svetlana Ya. 9 Külske, Christof 9 Molchanov, Stanislav Alekseevich 9 Picco, Pierre 9 Schonmann, Roberto Henrique 9 Stein, Daniel L. 9 Tassion, Vincent 9 Toninelli, Fabio Lucio 9 Yau, Horng-Tzer 8 Balogh, József 8 Banasiak, Jacek 8 Chen, Thomas M. 8 Damron, Michael 8 Häggström, Olle 8 Heydenreich, Markus 8 Joye, Alain 8 Nachmias, Asaf 8 Sadel, Christian 8 Schulz-Baldes, Hermann 8 Sly, Allan 8 Zegarlinski, Boguslaw 7 Albeverio, Sergio A. 7 Bodineau, Thierry 7 Ding, Jian 7 Erdős, László 7 Giacomin, Giambattista 7 Hulshof, Tim 7 Itoi, Chigak 7 Kesten, Harry 7 Kuwae, Kazuhiro 7 Mastropietro, Vieri 7 Müller, Peter 7 Peres, Yuval 7 Raoufi, Aran 7 Sabri, Mostafa 7 Sanchis, Rémy 7 Schramm, Oded 7 Shlosman, Senya B. 7 Skrypnik, Igor Igorievich 7 Starr, Shannon L. 7 Stollmann, Peter 7 Talagrand, Michel 7 Zhao, Zhongxin 6 Alexander, Kenneth S. 6 Anantharaman, Nalini 6 Borgs, Christian 6 Campanino, Massimo 6 Chen, Wei-Kuo 6 Chen, Zhen-Qing 6 Hammond, Alan 6 Jagannath, Aukosh 6 Keller, Matthias 6 Kirsch, Werner 6 Lacoin, Hubert 6 Lyons, Russell ...and 1,410 more Authors
all top 5

Cited in 229 Serials

 252 Journal of Statistical Physics 211 Communications in Mathematical Physics 89 Probability Theory and Related Fields 85 Journal of Mathematical Physics 81 The Annals of Probability 57 Journal of Functional Analysis 48 Annales Henri Poincaré 32 Stochastic Processes and their Applications 30 The Annals of Applied Probability 29 Reviews in Mathematical Physics 22 Journal of Mathematical Analysis and Applications 21 Letters in Mathematical Physics 20 Transactions of the American Mathematical Society 17 Proceedings of the American Mathematical Society 16 Journal of Statistical Mechanics: Theory and Experiment 15 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 14 Mathematical Physics, Analysis and Geometry 14 Journal of Spectral Theory 12 Duke Mathematical Journal 12 Journal of Differential Equations 12 Random Structures & Algorithms 11 Communications in Partial Differential Equations 11 Journal of the European Mathematical Society (JEMS) 10 Inventiones Mathematicae 10 Comptes Rendus. Mathématique. Académie des Sciences, Paris 9 Communications on Pure and Applied Mathematics 9 Journal of Theoretical Probability 9 Electronic Journal of Probability 8 Journal de Mathématiques Pures et Appliquées. Neuvième Série 8 Bulletin of the American Mathematical Society. New Series 7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 7 Annales de l’Institut Henri Poincaré. Physique Théorique 7 Journal of Physics A: Mathematical and Theoretical 6 International Journal of Modern Physics B 6 Reports on Mathematical Physics 6 Journal of the American Mathematical Society 6 Potential Analysis 6 Combinatorics, Probability and Computing 6 Physical Review Letters 5 Journal d’Analyse Mathématique 5 Nuclear Physics. B 5 Physics Reports 5 Advances in Mathematics 5 Journal of Applied Probability 5 Journal of Soviet Mathematics 5 Mathematische Annalen 5 Mathematische Nachrichten 5 Statistics & Probability Letters 5 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 5 Physica D 5 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 5 Geometric and Functional Analysis. GAFA 5 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 5 Probability Surveys 4 Modern Physics Letters B 4 Israel Journal of Mathematics 4 Mathematical Proceedings of the Cambridge Philosophical Society 4 Physica A 4 Transport Theory and Statistical Physics 4 Acta Mathematica 4 Theoretical Computer Science 4 Ergodic Theory and Dynamical Systems 4 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 4 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 4 Journal of Mathematical Sciences (New York) 4 Electronic Communications in Probability 4 Abstract and Applied Analysis 4 Annals of Mathematics. Second Series 3 Archive for Rational Mechanics and Analysis 3 Discrete Applied Mathematics 3 Discrete Mathematics 3 Mathematical Methods in the Applied Sciences 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Arkiv för Matematik 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 The Annals of Statistics 3 Journal of Combinatorial Theory. Series A 3 Linear Algebra and its Applications 3 Proceedings of the National Academy of Sciences of the United States of America 3 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 3 Positivity 3 Communications in Contemporary Mathematics 3 Journal of High Energy Physics 3 ALEA. Latin American Journal of Probability and Mathematical Statistics 3 Advances in Mathematical Physics 2 Applicable Analysis 2 Bulletin of the Australian Mathematical Society 2 Mathematical Notes 2 Physics Letters. A 2 Theoretical and Mathematical Physics 2 Mathematics of Computation 2 Annales de l’Institut Fourier 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 2 Publications Mathématiques 2 Journal für die Reine und Angewandte Mathematik 2 Mathematische Zeitschrift 2 Rendiconti del Seminario Matematico della Università di Padova 2 Statistica Neerlandica 2 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 2 Stochastic Analysis and Applications ...and 129 more Serials
all top 5

Cited in 55 Fields

 1,007 Statistical mechanics, structure of matter (82-XX) 771 Probability theory and stochastic processes (60-XX) 271 Partial differential equations (35-XX) 254 Quantum theory (81-XX) 242 Operator theory (47-XX) 130 Combinatorics (05-XX) 55 Dynamical systems and ergodic theory (37-XX) 48 Ordinary differential equations (34-XX) 38 Functional analysis (46-XX) 37 Linear and multilinear algebra; matrix theory (15-XX) 30 Potential theory (31-XX) 30 Computer science (68-XX) 27 Integral equations (45-XX) 25 Measure and integration (28-XX) 25 Global analysis, analysis on manifolds (58-XX) 19 Biology and other natural sciences (92-XX) 14 Fluid mechanics (76-XX) 11 Convex and discrete geometry (52-XX) 11 Numerical analysis (65-XX) 11 Mechanics of particles and systems (70-XX) 11 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 10 Functions of a complex variable (30-XX) 10 Difference and functional equations (39-XX) 10 Statistics (62-XX) 9 Number theory (11-XX) 9 Differential geometry (53-XX) 8 History and biography (01-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 7 Classical thermodynamics, heat transfer (80-XX) 6 General and overarching topics; collections (00-XX) 6 $$K$$-theory (19-XX) 6 Group theory and generalizations (20-XX) 6 Real functions (26-XX) 6 Mechanics of deformable solids (74-XX) 6 Operations research, mathematical programming (90-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Optics, electromagnetic theory (78-XX) 5 Information and communication theory, circuits (94-XX) 4 Special functions (33-XX) 4 Approximations and expansions (41-XX) 3 Mathematical logic and foundations (03-XX) 3 Topological groups, Lie groups (22-XX) 3 Relativity and gravitational theory (83-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Algebraic geometry (14-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Abstract harmonic analysis (43-XX) 2 Integral transforms, operational calculus (44-XX) 2 Geometry (51-XX) 2 General topology (54-XX) 2 Algebraic topology (55-XX) 1 Field theory and polynomials (12-XX) 1 Associative rings and algebras (16-XX) 1 Sequences, series, summability (40-XX) 1 Systems theory; control (93-XX)

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