## Aizenman, Michael

Compute Distance To:
 Author ID: aizenman.michael Published as: Aizenman, Michael; Aizenman, M. Homepage: https://www.princeton.edu/~aizenman/ External Links: MGP · Wikidata · Math-Net.Ru · dblp · GND · IdRef
 Documents Indexed: 82 Publications since 1975, including 1 Book 2 Contributions as Editor Biographic References: 2 Publications Co-Authors: 55 Co-Authors with 68 Joint Publications 1,706 Co-Co-Authors
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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 Duminil-Copin, Hugo 4 Goldstein, Sheldon 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 Z. 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 Klein, Abel 1 Molchanov, Stanislav Alekseevich 1 Nachtergaele, Bruno 1 Ruelle, David Pierre 1 Russo, Lucio 1 Ruzmaikina, Anastasia A. 1 Sanches Fernandes, K. 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 2 Annals of Mathematics. Second Series 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 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

 61 Statistical mechanics, structure of matter (82-XX) 42 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 Open

74 Publications have been cited 2,671 times in 1,766 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
Random operators. Disorder effects on quantum spectra and dynamics. Zbl 1333.82001
Aizenman, Michael; Warzel, Simone
2015
Finite-volume fractional-moment criteria for Anderson localization. Zbl 1038.82038
Aizenman, Michael; Schenker, Jeffrey H.; Friedrich, Roland M.; Hundertmark, Dirk
2001
Some rigorous results on the Sherrington-Kirkpatrick spin glass model. Zbl 1108.82312
Aizenman, M.; Lebowitz, J. L.; Ruelle, D.
1987
Rounding effects of quenched randomness on first-order phase transitions. Zbl 0714.60090
Aizenman, Michael; Wehr, Jan
1990
Convergence to equilibrium in a system of reacting polymers. Zbl 0458.76062
Aizenman, Michael; Bak, Thor A.
1979
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 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
Hölder regularity and dimension bounds for random curves. Zbl 0944.60022
Aizenman, M.; Burchard, A.
1999
On the critical behavior of the magnetization in high-dimensional Ising models. Zbl 0629.60106
Aizenman, M.; Fernández, R.
1986
Geometric aspects of quantum spin states. Zbl 0799.58087
Aizenman, Michael; Nachtergaele, Bruno
1994
Stability of the absolutely continuous spectrum of random Schrödinger operators on tree graphs. Zbl 1169.82007
Aizenman, Michael; Sims, Robert; Warzel, Simone
2006
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
Random currents and continuity of Ising model’s spontaneous magnetization. Zbl 1315.82004
Aizenman, Michael; Duminil-Copin, Hugo; Sidoravicius, Vladas
2015
Percolation critical exponents under the triangle condition. Zbl 0747.60093
Barsky, D. J.; Aizenman, M.
1991
Resonant delocalization for random Schrödinger operators on tree graphs. Zbl 1267.47064
Aizenman, Michael; Warzel, Simone
2013
On the structure of quasi-stationary competing particle systems. Zbl 1177.60050
Arguin, Louis-Pierre; Aizenman, Michael
2009
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
On vector fields as generators of flows: A counterexample to Nelson’s conjecture. Zbl 0394.28012
Aizenman, Michael
1978
Fluctuations of extensive functions of quenched random couplings. Zbl 0718.60129
Wehr, Jan; Aizenman, Michael
1990
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
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
Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs. Zbl 1278.81090
Aizenman, Michael; Warzel, Simone
2012
Critical exponents for long-range interactions. Zbl 0658.60136
Aizenman, Michael; Fernández, Roberto
1988
On Bernoulli decompositions for random variables, concentration bounds, and spectral localization. Zbl 1152.60020
Aizenman, Michael; Germinet, François; Klein, Abel; Warzel, Simone
2009
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
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
Mean-field spin glass models from the cavity-ROSt perspective. Zbl 1175.82033
Aizenman, Michael; Sims, Robert; Starr, Shannon L.
2007
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
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
Marginal triviality of the scaling limits of critical 4D Ising and $$\phi_4^4$$ models. Zbl 07375202
Aizenman, Michael; Duminil-Copin, Hugo
2021
Emergent planarity in two-dimensional Ising models with finite-range interactions. Zbl 1417.82022
Aizenman, Michael; Duminil-Copin, Hugo; Tassion, Vincent; Warzel, Simone
2019
Resonances and partial delocalization on the complete graph. Zbl 1329.81192
Aizenman, Michael; Shamis, Mira; Warzel, Simone
2015
Complete dynamical localization in disordered quantum multi-particle systems. Zbl 1205.82089
Aizenman, Michael; Warzel, Simone
2010
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
Persistence under weak disorder of AC spectra of quasi-periodic Schrödinger operators on trees graphs. Zbl 1124.47027
Aizenman, M.; Warzel, S.
2005
On the critical behavior at the lower phase transition of the contact process. Zbl 1160.60332
Aizenman, Michael; Jung, Paul
2007
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
Symmetry breaking in quasi-1D Coulomb systems. Zbl 1209.82025
Aizenman, Michael; Jansen, Sabine; Jung, Paul
2010
Exponential decay of correlations in the $$2D$$ random field Ising model. Zbl 1460.60105
Aizenman, Michael; Harel, Matan; Peled, Ron
2020
A power-law upper bound on the correlations in the 2D random field Ising model. Zbl 1447.82005
Aizenman, Michael; Peled, Ron
2019
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
Rigorous studies of critical behavior. Zbl 0667.60102
Aizenman, Michael
1986
General results in percolation theory. Zbl 0639.60099
Aizenman, Michael
1987
Stochastic geometry in statistical mechanics and quantum field theory. Zbl 0564.60012
Aizenman, Michael
1984
Dimerization and Néel order in different quantum spin chains through a shared loop representation. Zbl 1453.82003
Aizenman, Michael; Duminil-Copin, Hugo; Warzel, Simone
2020
Boosted Simon-Wolff spectral criterion and resonant delocalization. Zbl 1387.47025
Aizenman, Michael; Warzel, Simone
2016
Matrix regularizing effects of Gaussian perturbations. Zbl 1360.60012
Aizenman, Michael; Peled, Ron; Schenker, Jeffrey; Shamis, Mira; Sodin, Sasha
2017
Pfaffian correlation functions of planar dimer covers. Zbl 1360.82016
Aizenman, Michael; Valcázar, Manuel Laínz; Warzel, Simone
2017
Kac-Ward formula and its extension to order-disorder correlators through a graph zeta function. Zbl 1405.82006
Aizenman, Michael; Warzel, Simone
2018
Marginal triviality of the scaling limits of critical 4D Ising and $$\phi_4^4$$ models. Zbl 07375202
Aizenman, Michael; Duminil-Copin, Hugo
2021
Exponential decay of correlations in the $$2D$$ random field Ising model. Zbl 1460.60105
Aizenman, Michael; Harel, Matan; Peled, Ron
2020
Dimerization and Néel order in different quantum spin chains through a shared loop representation. Zbl 1453.82003
Aizenman, Michael; Duminil-Copin, Hugo; Warzel, Simone
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
Matrix regularizing effects of Gaussian perturbations. Zbl 1360.60012
Aizenman, Michael; Peled, Ron; Schenker, Jeffrey; Shamis, Mira; Sodin, Sasha
2017
Pfaffian correlation functions of planar dimer covers. Zbl 1360.82016
Aizenman, Michael; Valcázar, Manuel Laínz; Warzel, Simone
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
Complete dynamical localization in disordered quantum multi-particle systems. Zbl 1205.82089
Aizenman, Michael; Warzel, Simone
2010
Symmetry breaking in quasi-1D Coulomb systems. Zbl 1209.82025
Aizenman, Michael; Jansen, Sabine; Jung, Paul
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
Localization bounds for an electron gas. Zbl 0953.82009
Aizenman, M.; Graf, G. M.
1998
On the stability of the quenched state in mean-field spin-glass models. Zbl 0963.82045
Aizenman, M.; Contucci, P.
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 1,599 Authors

 40 Aizenman, Michael 30 Newman, Charles Michael 28 Klein, Abel 26 Duminil-Copin, Hugo 24 Warzel, Simone 23 Chayes, Lincoln 17 Bollobás, Béla 17 Chayes, Jennifer Tour 17 Chulaevsky, Victor 17 Slade, Gordon 17 van der Hofstad, Remco W. 16 Camia, Federico 16 Germinet, François 16 Stolz, Gunter 15 Elgart, Alexander 15 van Enter, Aernout C. D. 14 Barra, Adriano 14 Grimmett, Geoffrey R. 14 Nachtergaele, Bruno 14 Panchenko, Dmitry 14 Schenker, Jeffrey H. 13 Arguin, Louis-Pierre 13 Hislop, Peter D. 13 Hutchcroft, Tom 13 Klopp, Frédéric 13 Veselić, Ivan 12 Björnberg, Jakob Erik 12 Chatterjee, Sourav 12 Contucci, Pierluigi 12 Ioffe, Dmitry 12 Kozma, Gady 12 Tassion, Vincent 12 Ueltschi, Daniel 11 Biskup, Marek 11 Gravner, Janko 11 Lebowitz, Joel Louis 11 Sakai, Akira 11 Sidoravicius, Vladas 11 Simon, Barry 11 Sims, Robert L. 11 Yau, Horng-Tzer 10 Crawford, Nicholas 10 Fröhlich, Jürg Martin 10 Molchanov, Stanislav Alekseevich 10 Morris, Robert D. 9 Cassandro, Marzio 9 Damanik, David 9 Hara, Takashi 9 Heydenreich, Markus 9 Jitomirskaya, Svetlana Yakovlevna 9 Külske, Christof 9 Picco, Pierre 9 Sabri, Mostafa 9 Sadel, Christian 9 Schonmann, Roberto Henrique 9 Stein, Daniel L. 9 Toninelli, Fabio Lucio 8 Albeverio, Sergio A. 8 Anantharaman, Nalini 8 Balogh, József 8 Banasiak, Jacek 8 Damron, Michael 8 Ding, Jian 8 Häggström, Olle 8 Joye, Alain 8 Mastropietro, Vieri 8 Nachmias, Asaf 8 Raoufi, Aran 8 Schulz-Baldes, Hermann 8 Zegarlinski, Boguslaw 8 Zhao, Zhongxin 7 Bodineau, Thierry 7 Chen, Wei-Kuo 7 Erdős, László 7 Giacomin, Giambattista 7 Güneysu, Batu 7 Holroyd, Alexander E. 7 Hulshof, Tim 7 Itoi, Chigak 7 Kesten, Harry 7 Kuwae, Kazuhiro 7 Mâagli, Habib 7 Müller, Peter 7 Sanchis, Rémy 7 Schramm, Oded 7 Shlosman, Senya B. 7 Skrypnik, Igor Igorievich 7 Sly, Allan 7 Starr, Shannon L. 7 Talagrand, Michel 6 Alexander, Kenneth S. 6 Borgs, Christian 6 Campanino, Massimo 6 Chen, Thomas M. 6 Chen, Zhen-Qing 6 Ekanga, Trésor 6 Garban, Christophe 6 Hammond, Alan 6 Hartarsky, Ivailo 6 Jagannath, Aukosh ...and 1,499 more Authors
all top 5

### Cited in 242 Serials

 263 Journal of Statistical Physics 227 Communications in Mathematical Physics 100 Probability Theory and Related Fields 88 Journal of Mathematical Physics 86 The Annals of Probability 60 Journal of Functional Analysis 53 Annales Henri Poincaré 34 Stochastic Processes and their Applications 33 Reviews in Mathematical Physics 33 The Annals of Applied Probability 24 Journal of Mathematical Analysis and Applications 23 Letters in Mathematical Physics 20 Transactions of the American Mathematical Society 20 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 20 Electronic Journal of Probability 19 Journal of Spectral Theory 17 Proceedings of the American Mathematical Society 17 Mathematical Physics, Analysis and Geometry 13 Inventiones Mathematicae 13 Journal of Differential Equations 13 Journal of the European Mathematical Society (JEMS) 12 Duke Mathematical Journal 12 Random Structures & Algorithms 12 Journal of Statistical Mechanics: Theory and Experiment 11 Communications in Partial Differential Equations 11 Comptes Rendus. Mathématique. Académie des Sciences, Paris 10 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 10 Journal of Theoretical Probability 10 Journal de Mathématiques Pures et Appliquées. Neuvième Série 9 Communications on Pure and Applied Mathematics 8 Bulletin of the American Mathematical Society. New Series 7 Annales de l’Institut Henri Poincaré. Physique Théorique 7 Potential Analysis 7 Combinatorics, Probability and Computing 7 Journal of Physics A: Mathematical and Theoretical 6 International Journal of Modern Physics B 6 Reports on Mathematical Physics 6 Advances in Mathematics 6 The Electronic Journal of Combinatorics 6 Electronic Communications in Probability 6 Physical Review Letters 6 ALEA. Latin American Journal of Probability and Mathematical Statistics 5 Archive for Rational Mechanics and Analysis 5 Journal d’Analyse Mathématique 5 Nuclear Physics. B 5 Physica A 5 Physics Reports 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 Journal of the American Mathematical Society 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 Journal of Mathematical Sciences (New York) 5 Annals of Mathematics. Second Series 5 Probability Surveys 4 Modern Physics Letters B 4 Israel Journal of Mathematics 4 Mathematical Proceedings of the Cambridge Philosophical Society 4 Transport Theory and Statistical Physics 4 Acta Mathematica 4 Theoretical Computer Science 4 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 4 Ergodic Theory and Dynamical Systems 4 Physica D 4 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 4 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 4 Abstract and Applied Analysis 4 Positivity 4 Advances in Mathematical Physics 3 Discrete Applied Mathematics 3 Discrete Mathematics 3 Mathematical Methods in the Applied Sciences 3 Theoretical and Mathematical Physics 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 The Journal of Geometric Analysis 3 Linear Algebra and its Applications 3 Proceedings of the National Academy of Sciences of the United States of America 3 Indagationes Mathematicae. New Series 3 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 3 Communications in Contemporary Mathematics 3 Brazilian Journal of Probability and Statistics 2 Applicable Analysis 2 Bulletin of the Australian Mathematical Society 2 Mathematical Notes 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 ...and 142 more Serials
all top 5

### Cited in 56 Fields

 1,085 Statistical mechanics, structure of matter (82-XX) 859 Probability theory and stochastic processes (60-XX) 307 Partial differential equations (35-XX) 290 Quantum theory (81-XX) 260 Operator theory (47-XX) 167 Combinatorics (05-XX) 58 Dynamical systems and ergodic theory (37-XX) 54 Ordinary differential equations (34-XX) 47 Functional analysis (46-XX) 43 Linear and multilinear algebra; matrix theory (15-XX) 34 Potential theory (31-XX) 33 Computer science (68-XX) 29 Global analysis, analysis on manifolds (58-XX) 27 Integral equations (45-XX) 26 Measure and integration (28-XX) 21 Biology and other natural sciences (92-XX) 18 Fluid mechanics (76-XX) 16 Differential geometry (53-XX) 14 Statistics (62-XX) 14 Numerical analysis (65-XX) 12 Functions of a complex variable (30-XX) 12 Convex and discrete geometry (52-XX) 12 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 11 Difference and functional equations (39-XX) 10 Harmonic analysis on Euclidean spaces (42-XX) 10 Mechanics of particles and systems (70-XX) 9 History and biography (01-XX) 9 Number theory (11-XX) 9 Classical thermodynamics, heat transfer (80-XX) 8 General and overarching topics; collections (00-XX) 7 Real functions (26-XX) 7 Mechanics of deformable solids (74-XX) 7 Information and communication theory, circuits (94-XX) 6 $$K$$-theory (19-XX) 6 Group theory and generalizations (20-XX) 6 Operations research, mathematical programming (90-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 4 Special functions (33-XX) 4 Approximations and expansions (41-XX) 4 Geometry (51-XX) 4 Optics, electromagnetic theory (78-XX) 4 Relativity and gravitational theory (83-XX) 3 Algebraic geometry (14-XX) 3 Topological groups, Lie groups (22-XX) 2 Mathematical logic and foundations (03-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Abstract harmonic analysis (43-XX) 2 Integral transforms, operational calculus (44-XX) 2 General topology (54-XX) 2 Algebraic topology (55-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Associative rings and algebras (16-XX) 1 Sequences, series, summability (40-XX) 1 Systems theory; control (93-XX)

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