Edit Profile Aizenman, Michael Compute Distance To: Compute 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 all top 5 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 all top 5 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 all top 5 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) Publications by Year all cited Publications top 5 cited Publications 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 0782.60044Aizenman, Michael; Molchanov, Stanislav 210 1993 Brownian motion and Harnack inequality for Schrödinger operators. Zbl 0459.60069Aizenman, M.; Simon, B. 183 1982 Discontinuity of the magnetization in one-dimensional \(1/| x-y| ^ 2\) Ising and Potts models. Zbl 1084.82514Aizenman, M.; Chayes, J. T.; Chayes, L.; Newman, C. M. 122 1988 Sharpness of the phase transition in percolation models. Zbl 0618.60098Aizenman, Michael; Barsky, David J. 120 1987 Geometric analysis of \(\phi^ 4\) fields and Ising models. I, II. Zbl 0533.58034Aizenman, Michael 107 1982 Localization at weak disorder: some elementary bounds. Zbl 0843.47039Aizenman, Michael 98 1994 Metastability effects in bootstrap percolation. Zbl 0656.60106Aizenman, M.; Lebowitz, J. L. 86 1988 Tree graph inequalities and critical behavior in percolation models. Zbl 0586.60096Aizenman, Michael; Newman, Charles M. 79 1984 Finite-volume fractional-moment criteria for Anderson localization. Zbl 1038.82038Aizenman, Michael; Schenker, Jeffrey H.; Friedrich, Roland M.; Hundertmark, Dirk 73 2001 Rounding effects of quenched randomness on first-order phase transitions. Zbl 0714.60090Aizenman, Michael; Wehr, Jan 71 1990 Some rigorous results on the Sherrington-Kirkpatrick spin glass model. Zbl 1108.82312Aizenman, M.; Lebowitz, J. L.; Ruelle, D. 66 1987 Random operators. Disorder effects on quantum spectra and dynamics. Zbl 1333.82001Aizenman, Michael; Warzel, Simone 62 2015 Convergence to equilibrium in a system of reacting polymers. Zbl 0458.76062Aizenman, Michael; Bak, Thor A. 62 1979 On the stability of the quenched state in mean-field spin-glass models. Zbl 0963.82045Aizenman, M.; Contucci, P. 60 1998 Moment analysis for localization in random Schrödinger operators. Zbl 1090.81026Aizenman, Michael; Elgart, Alexander; Naboko, Serguei; Schenker, Jeffrey H.; Stolz, Gunter 57 2006 Uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolation. Zbl 0642.60102Aizenman, M.; Kesten, H.; Newman, C. M. 55 1987 Discontinuity of the percolation density in one dimensional \(1/| x- y| ^ 2\) percolation models. Zbl 0613.60097Aizenman, M.; Newman, C. M. 54 1986 Localization bounds for an electron gas. Zbl 0953.82009Aizenman, M.; Graf, G. M. 53 1998 On the critical behavior of the magnetization in high-dimensional Ising models. Zbl 0629.60106Aizenman, M.; Fernández, R. 48 1986 Hölder regularity and dimension bounds for random curves. Zbl 0944.60022Aizenman, M.; Burchard, A. 46 1999 Stability of the absolutely continuous spectrum of random Schrödinger operators on tree graphs. Zbl 1169.82007Aizenman, Michael; Sims, Robert; Warzel, Simone 45 2006 Geometric aspects of quantum spin states. Zbl 0799.58087Aizenman, Michael; Nachtergaele, Bruno 44 1994 On a sharp transition from area law to perimeter law in a system of random surfaces. Zbl 0529.60099Aizenman, M.; Chayes, J. T.; Chayes, L.; Fröhlich, J.; Russo, L. 44 1983 Localization bounds for multiparticle systems. Zbl 1186.82055Aizenman, Michael; Warzel, Simone 37 2009 Percolation critical exponents under the triangle condition. Zbl 0747.60093Barsky, D. J.; Aizenman, M. 37 1991 On the structure of quasi-stationary competing particle systems. Zbl 1177.60050Arguin, Louis-Pierre; Aizenman, Michael 35 2009 Random currents and continuity of Ising model’s spontaneous magnetization. Zbl 1315.82004Aizenman, Michael; Duminil-Copin, Hugo; Sidoravicius, Vladas 32 2015 Resonant delocalization for random Schrödinger operators on tree graphs. Zbl 1267.47064Aizenman, Michael; Warzel, Simone 32 2013 Characterization of invariant measures at the leading edge for competing particle systems. Zbl 1096.60042Ruzmaikina, Anastasia; Aizenman, Michael 31 2005 Absolutely continuous spectra of quantum tree graphs with weak disorder. Zbl 1233.34009Aizenman, Michael; Sims, Robert; Warzel, Simone 27 2006 On the number of incipient spanning clusters. Zbl 0925.82112Aizenman, Michael 26 1997 Rapid convergence to equilibrium of stochastic Ising models in the Dobrushin Shlosman regime. Zbl 0621.60118Aizenman, M.; Holley, R. 25 1987 The Canophy graph and level statistics for random operators on trees. Zbl 1138.47032Aizenman, Michael; Warzel, Simone 21 2006 Fluctuations of extensive functions of quenched random couplings. Zbl 0718.60129Wehr, Jan; Aizenman, Michael 20 1990 On vector fields as generators of flows: A counterexample to Nelson’s conjecture. Zbl 0394.28012Aizenman, Michael 20 1978 The intersection of Brownian paths as a case study of a renormalization group method for quantum field theory. Zbl 0573.60076Aizenman, Michael 18 1985 The creation of spectral gaps by graph decoration. Zbl 0990.47006Schenker, Jeffrey H.; Aizenman, Michael 17 2000 Bose-Einstein condensation as a quantum phase transition in an optical lattice. Zbl 1170.82325Aizenman, M.; Lieb, E. H.; Seiringer, R.; Solovej, J. P.; Yngvason, J. 16 2006 Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs. Zbl 1278.81090Aizenman, Michael; Warzel, Simone 15 2012 Scaling limits for minimal and random spanning trees in two dimensions. Zbl 0939.60031Aizenman, Michael; Burchard, Almut; Newman, Charles M.; Wilson, David B. 15 1999 On Bernoulli decompositions for random variables, concentration bounds, and spectral localization. Zbl 1152.60020Aizenman, Michael; Germinet, François; Klein, Abel; Warzel, Simone 12 2009 Mean-field spin glass models from the cavity-ROSt perspective. Zbl 1175.82033Aizenman, Michael; Sims, Robert; Starr, Shannon L. 12 2007 Critical exponents for long-range interactions. Zbl 0658.60136Aizenman, Michael; Fernández, Roberto 12 1988 Conditional equilibrium and the equivalence of microcanonical and grandcanonical ensembles in the thermodynamic limit. Zbl 0391.60097Aizenman, Michael; Goldstein, Sheldon; Lebowitz, Joel L. 12 1978 Scaling limit for the incipient spanning clusters. Zbl 0941.74013Aizenman, Michael 11 1998 On the slow decay of \(O(2)\) correlations in the absence of topological excitations: Remark on the Patrascioiu-Seiler model. Zbl 0838.60096Aizenman, Michael 10 1994 Precolation of the minority spins in high-dimensional Ising models. Zbl 0960.82503Aizenman, M.; Bricmont, J.; Lebowitz, J. L. 9 1987 Bounded fluctuations and translation symmetry breaking in one-dimensional particle systems. Zbl 0999.82030Aizenman, M.; Goldstein, S.; Lebowitz, J. L. 8 2001 A sufficient condition for the avoidance of sets by measure preserving flows in \(\mathbb R^ n\). Zbl 0471.28015Aizenman, Michael 8 1978 Ergodic properties of an infinite one dimensional hard rod system. Zbl 0352.60073Aizenman, Michael; Goldstein, Sheldon; Lebowitz, Joel L. 8 1975 On the ubiquity of the Cauchy distribution in spectral problems. Zbl 1330.60042Aizenman, Michael; Warzel, Simone 7 2015 Resonances and partial delocalization on the complete graph. Zbl 1329.81192Aizenman, Michael; Shamis, Mira; Warzel, Simone 6 2015 Proof of rounding by quenched disorder of first order transitions in low-dimensional quantum systems. Zbl 1290.82014Aizenman, Michael; Greenblatt, Rafael L.; Lebowitz, Joel L. 6 2012 On the critical behavior at the lower phase transition of the contact process. Zbl 1160.60332Aizenman, Michael; Jung, Paul 5 2007 Fluctuation-based proof of the stability of ac spectra of random operators on tree graphs. Zbl 1111.82022Aizenman, Michael; Sims, Robert; Warzel, Simone 5 2006 Ergodic properties of infinite systems. Zbl 0316.28008Goldstein, Sheldon; Lebowitz, Joel L.; Aizenman, Michael 5 1975 On the joint distribution of energy levels of random Schrödinger operators. Zbl 1156.47037Aizenman, Michael; Warzel, Simone 4 2009 Emergent planarity in two-dimensional Ising models with finite-range interactions. Zbl 1417.82022Aizenman, Michael; Duminil-Copin, Hugo; Tassion, Vincent; Warzel, Simone 3 2019 Symmetry breaking in quasi-1D Coulomb systems. Zbl 1209.82025Aizenman, Michael; Jansen, Sabine; Jung, Paul 3 2010 Complete dynamical localization in disordered quantum multi-particle systems. Zbl 1205.82089Aizenman, Michael; Warzel, Simone 3 2010 Exponential decay of correlations in the \(2D\) random field Ising model. Zbl 07239465Aizenman, Michael; Harel, Matan; Peled, Ron 2 2020 Persistence under weak disorder of AC spectra of quasi-periodic Schrödinger operators on trees graphs. Zbl 1124.47027Aizenman, M.; Warzel, S. 2 2005 Rigorous studies of critical behavior. II. Zbl 0662.60114Aizenman, Michael 2 1985 Positive linear maps which are order bounded on \(C^*\) subalgebras. Zbl 0397.46058Aizenman, Michael; Davies, E. Brian; Lieb, Elliott H. 2 1978 A power-law upper bound on the correlations in the 2D random field Ising model. Zbl 1447.82005Aizenman, Michael; Peled, Ron 1 2019 Kac-Ward formula and its extension to order-disorder correlators through a graph zeta function. Zbl 1405.82006Aizenman, Michael; Warzel, Simone 1 2018 Pfaffian correlation functions of planar dimer covers. Zbl 1360.82016Aizenman, Michael; Valcázar, Manuel Laínz; Warzel, Simone 1 2017 Matrix regularizing effects of Gaussian perturbations. Zbl 1360.60012Aizenman, Michael; Peled, Ron; Schenker, Jeffrey; Shamis, Mira; Sodin, Sasha 1 2017 Boosted Simon-Wolff spectral criterion and resonant delocalization. Zbl 1387.47025Aizenman, Michael; Warzel, Simone 1 2016 General results in percolation theory. Zbl 0639.60099Aizenman, Michael 1 1987 Rigorous studies of critical behavior. Zbl 0667.60102Aizenman, Michael 1 1986 Stochastic geometry in statistical mechanics and quantum field theory. Zbl 0564.60012Aizenman, Michael 1 1984 Exponential decay of correlations in the \(2D\) random field Ising model. Zbl 07239465Aizenman, Michael; Harel, Matan; Peled, Ron 2 2020 Emergent planarity in two-dimensional Ising models with finite-range interactions. Zbl 1417.82022Aizenman, Michael; Duminil-Copin, Hugo; Tassion, Vincent; Warzel, Simone 3 2019 A power-law upper bound on the correlations in the 2D random field Ising model. Zbl 1447.82005Aizenman, Michael; Peled, Ron 1 2019 Kac-Ward formula and its extension to order-disorder correlators through a graph zeta function. Zbl 1405.82006Aizenman, Michael; Warzel, Simone 1 2018 Pfaffian correlation functions of planar dimer covers. Zbl 1360.82016Aizenman, Michael; Valcázar, Manuel Laínz; Warzel, Simone 1 2017 Matrix regularizing effects of Gaussian perturbations. Zbl 1360.60012Aizenman, Michael; Peled, Ron; Schenker, Jeffrey; Shamis, Mira; Sodin, Sasha 1 2017 Boosted Simon-Wolff spectral criterion and resonant delocalization. Zbl 1387.47025Aizenman, Michael; Warzel, Simone 1 2016 Random operators. Disorder effects on quantum spectra and dynamics. Zbl 1333.82001Aizenman, Michael; Warzel, Simone 62 2015 Random currents and continuity of Ising model’s spontaneous magnetization. Zbl 1315.82004Aizenman, Michael; Duminil-Copin, Hugo; Sidoravicius, Vladas 32 2015 On the ubiquity of the Cauchy distribution in spectral problems. Zbl 1330.60042Aizenman, Michael; Warzel, Simone 7 2015 Resonances and partial delocalization on the complete graph. Zbl 1329.81192Aizenman, Michael; Shamis, Mira; Warzel, Simone 6 2015 Resonant delocalization for random Schrödinger operators on tree graphs. Zbl 1267.47064Aizenman, Michael; Warzel, Simone 32 2013 Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs. Zbl 1278.81090Aizenman, Michael; Warzel, Simone 15 2012 Proof of rounding by quenched disorder of first order transitions in low-dimensional quantum systems. Zbl 1290.82014Aizenman, Michael; Greenblatt, Rafael L.; Lebowitz, Joel L. 6 2012 Symmetry breaking in quasi-1D Coulomb systems. Zbl 1209.82025Aizenman, Michael; Jansen, Sabine; Jung, Paul 3 2010 Complete dynamical localization in disordered quantum multi-particle systems. Zbl 1205.82089Aizenman, Michael; Warzel, Simone 3 2010 Localization bounds for multiparticle systems. Zbl 1186.82055Aizenman, Michael; Warzel, Simone 37 2009 On the structure of quasi-stationary competing particle systems. Zbl 1177.60050Arguin, Louis-Pierre; Aizenman, Michael 35 2009 On Bernoulli decompositions for random variables, concentration bounds, and spectral localization. Zbl 1152.60020Aizenman, Michael; Germinet, François; Klein, Abel; Warzel, Simone 12 2009 On the joint distribution of energy levels of random Schrödinger operators. Zbl 1156.47037Aizenman, Michael; Warzel, Simone 4 2009 Mean-field spin glass models from the cavity-ROSt perspective. Zbl 1175.82033Aizenman, Michael; Sims, Robert; Starr, Shannon L. 12 2007 On the critical behavior at the lower phase transition of the contact process. Zbl 1160.60332Aizenman, Michael; Jung, Paul 5 2007 Moment analysis for localization in random Schrödinger operators. Zbl 1090.81026Aizenman, Michael; Elgart, Alexander; Naboko, Serguei; Schenker, Jeffrey H.; Stolz, Gunter 57 2006 Stability of the absolutely continuous spectrum of random Schrödinger operators on tree graphs. Zbl 1169.82007Aizenman, Michael; Sims, Robert; Warzel, Simone 45 2006 Absolutely continuous spectra of quantum tree graphs with weak disorder. Zbl 1233.34009Aizenman, Michael; Sims, Robert; Warzel, Simone 27 2006 The Canophy graph and level statistics for random operators on trees. Zbl 1138.47032Aizenman, Michael; Warzel, Simone 21 2006 Bose-Einstein condensation as a quantum phase transition in an optical lattice. Zbl 1170.82325Aizenman, M.; Lieb, E. H.; Seiringer, R.; Solovej, J. P.; Yngvason, J. 16 2006 Fluctuation-based proof of the stability of ac spectra of random operators on tree graphs. Zbl 1111.82022Aizenman, Michael; Sims, Robert; Warzel, Simone 5 2006 Characterization of invariant measures at the leading edge for competing particle systems. Zbl 1096.60042Ruzmaikina, Anastasia; Aizenman, Michael 31 2005 Persistence under weak disorder of AC spectra of quasi-periodic Schrödinger operators on trees graphs. Zbl 1124.47027Aizenman, M.; Warzel, S. 2 2005 Finite-volume fractional-moment criteria for Anderson localization. Zbl 1038.82038Aizenman, Michael; Schenker, Jeffrey H.; Friedrich, Roland M.; Hundertmark, Dirk 73 2001 Bounded fluctuations and translation symmetry breaking in one-dimensional particle systems. Zbl 0999.82030Aizenman, M.; Goldstein, S.; Lebowitz, J. L. 8 2001 The creation of spectral gaps by graph decoration. Zbl 0990.47006Schenker, Jeffrey H.; Aizenman, Michael 17 2000 Hölder regularity and dimension bounds for random curves. Zbl 0944.60022Aizenman, M.; Burchard, A. 46 1999 Scaling limits for minimal and random spanning trees in two dimensions. Zbl 0939.60031Aizenman, Michael; Burchard, Almut; Newman, Charles M.; Wilson, David B. 15 1999 On the stability of the quenched state in mean-field spin-glass models. Zbl 0963.82045Aizenman, M.; Contucci, P. 60 1998 Localization bounds for an electron gas. Zbl 0953.82009Aizenman, M.; Graf, G. M. 53 1998 Scaling limit for the incipient spanning clusters. Zbl 0941.74013Aizenman, Michael 11 1998 On the number of incipient spanning clusters. Zbl 0925.82112Aizenman, Michael 26 1997 Localization at weak disorder: some elementary bounds. Zbl 0843.47039Aizenman, Michael 98 1994 Geometric aspects of quantum spin states. Zbl 0799.58087Aizenman, Michael; Nachtergaele, Bruno 44 1994 On the slow decay of \(O(2)\) correlations in the absence of topological excitations: Remark on the Patrascioiu-Seiler model. Zbl 0838.60096Aizenman, Michael 10 1994 Localization at large disorder and at extreme energies: an elementary derivation. Zbl 0782.60044Aizenman, Michael; Molchanov, Stanislav 210 1993 Percolation critical exponents under the triangle condition. Zbl 0747.60093Barsky, D. J.; Aizenman, M. 37 1991 Rounding effects of quenched randomness on first-order phase transitions. Zbl 0714.60090Aizenman, Michael; Wehr, Jan 71 1990 Fluctuations of extensive functions of quenched random couplings. Zbl 0718.60129Wehr, Jan; Aizenman, Michael 20 1990 Discontinuity of the magnetization in one-dimensional \(1/| x-y| ^ 2\) Ising and Potts models. Zbl 1084.82514Aizenman, M.; Chayes, J. T.; Chayes, L.; Newman, C. M. 122 1988 Metastability effects in bootstrap percolation. Zbl 0656.60106Aizenman, M.; Lebowitz, J. L. 86 1988 Critical exponents for long-range interactions. Zbl 0658.60136Aizenman, Michael; Fernández, Roberto 12 1988 Sharpness of the phase transition in percolation models. Zbl 0618.60098Aizenman, Michael; Barsky, David J. 120 1987 Some rigorous results on the Sherrington-Kirkpatrick spin glass model. Zbl 1108.82312Aizenman, M.; Lebowitz, J. L.; Ruelle, D. 66 1987 Uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolation. Zbl 0642.60102Aizenman, M.; Kesten, H.; Newman, C. M. 55 1987 Rapid convergence to equilibrium of stochastic Ising models in the Dobrushin Shlosman regime. Zbl 0621.60118Aizenman, M.; Holley, R. 25 1987 Precolation of the minority spins in high-dimensional Ising models. Zbl 0960.82503Aizenman, M.; Bricmont, J.; Lebowitz, J. L. 9 1987 General results in percolation theory. Zbl 0639.60099Aizenman, Michael 1 1987 Discontinuity of the percolation density in one dimensional \(1/| x- y| ^ 2\) percolation models. Zbl 0613.60097Aizenman, M.; Newman, C. M. 54 1986 On the critical behavior of the magnetization in high-dimensional Ising models. Zbl 0629.60106Aizenman, M.; Fernández, R. 48 1986 Rigorous studies of critical behavior. Zbl 0667.60102Aizenman, Michael 1 1986 The intersection of Brownian paths as a case study of a renormalization group method for quantum field theory. Zbl 0573.60076Aizenman, Michael 18 1985 Rigorous studies of critical behavior. II. Zbl 0662.60114Aizenman, Michael 2 1985 Tree graph inequalities and critical behavior in percolation models. Zbl 0586.60096Aizenman, Michael; Newman, Charles M. 79 1984 Stochastic geometry in statistical mechanics and quantum field theory. Zbl 0564.60012Aizenman, Michael 1 1984 On a sharp transition from area law to perimeter law in a system of random surfaces. Zbl 0529.60099Aizenman, M.; Chayes, J. T.; Chayes, L.; Fröhlich, J.; Russo, L. 44 1983 Brownian motion and Harnack inequality for Schrödinger operators. Zbl 0459.60069Aizenman, M.; Simon, B. 183 1982 Geometric analysis of \(\phi^ 4\) fields and Ising models. I, II. Zbl 0533.58034Aizenman, Michael 107 1982 Convergence to equilibrium in a system of reacting polymers. Zbl 0458.76062Aizenman, Michael; Bak, Thor A. 62 1979 On vector fields as generators of flows: A counterexample to Nelson’s conjecture. Zbl 0394.28012Aizenman, Michael 20 1978 Conditional equilibrium and the equivalence of microcanonical and grandcanonical ensembles in the thermodynamic limit. Zbl 0391.60097Aizenman, Michael; Goldstein, Sheldon; Lebowitz, Joel L. 12 1978 A sufficient condition for the avoidance of sets by measure preserving flows in \(\mathbb R^ n\). Zbl 0471.28015Aizenman, Michael 8 1978 Positive linear maps which are order bounded on \(C^*\) subalgebras. Zbl 0397.46058Aizenman, Michael; Davies, E. Brian; Lieb, Elliott H. 2 1978 Ergodic properties of an infinite one dimensional hard rod system. Zbl 0352.60073Aizenman, Michael; Goldstein, Sheldon; Lebowitz, Joel L. 8 1975 Ergodic properties of infinite systems. Zbl 0316.28008Goldstein, Sheldon; Lebowitz, Joel L.; Aizenman, Michael 5 1975 all cited Publications top 5 cited Publications 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) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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