!!Michael Aizenman - Selected Publications
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M. Aizenman, S. Warzel. Random Operators: Disorder Effects on Quantum Spectra and Dynamics (Grad. Studies in Mathematics, AMS 2015).\\
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M. Aizenman, S. Warzel: A Boosted Simon-Wolff Spectral Criterion and Resonant Delocalization. Commun. Pure Appl. Math. (2015) doi:10.1002/cpa.21625.\\
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M. Aizenman, H. Duminil-Copin and V. Sidoravicius) Random Currents and Continuity of Ising Model’s Spontaneous Magnetization, Comm. Math. Phys. 334, 719 (2015).\\
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M. Aizenman, S. Warzel: On the ubiquity of the Cauchy distribution in spectral problems, Probab. Theory Relat. Fields 163, 61 (2015).\\
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M. Aizenman and S. Warzel.  Resonant delocalization for random Schrödinger operators on tree graphs, J.  Euro. Math. Soc. 15, 1167 (2013).   \\
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M. Aizenman, R.L. Greenblatt and J.L. Lebowitz.  Proof of Rounding by Quenched Disorder of First Order Transitions in Low-Dimensional Quantum Systems. J. Math. Phys. 53, 023301 (2012).  \\
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M. Aizenman and S. Warzel. Absence of mobility edge for the Anderson random potential on tree graphs at weak disorder. Euro. Phys. Lett. 96, 37004 (2011).\\
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M. Aizenman, A. Elgart, S. Naboko, G. Stoltz, and J.H. Schenker.  Moment Analysis for Localization in Random Schrödinger Operators. Invent. Mathematicae 163, 343 (2006).\\
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A. Ruzmaikina and M. Aizenman. Characterization of Invariant Measures at the Leading Edge for Competing Particle Systems. Ann. Probab. 33, 82, (2005).\\
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M. Aizenman, E.H. Lieb, R. Seiringer, J.P. Solovej, and J. Yngvason. Bose-Einstein Quantum Phase Transition in an Optical Lattice Model. Phys. Rev. A 70, 023612 (2004).\\
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M. Aizenman,  R. Sims and S.L. Starr. Extended variational principle for the Sherrington-Kirkpatrick spin-glass model. Phys. Rev. B 68, 214403 (2003).\\
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M. Aizenman and A. Burchard. Hölder Regularity and Dimension Bounds for Random Curves. Duke Math. J. 99, 419 (1999). \\
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M. Aizenman, A. Aharony and B. Duplantier.  Connectivity Exponents and External Perimeter in 2D Independent Percolation Models. Phys. Rev. Lett. 83, 1359 (1999).\\
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M. Aizenman and B. Nachtergaele. Geometric Aspects of Quantum Spin States. Comm. Math. Phys. 164, 17 (1994).\\
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M. Aizenman and S. Molchanov. Localization at Large Disorder and at Extreme Energies: an Elementary Derivation. Comm. Math. Phys. 157, 245 (1993).\\
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D. Barsky and M. Aizenman.  Percolation Critical Exponents Under the Triangle Condition. Ann. Prob. 13, 1520 (1991).\\
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M. Aizenman and J. Wehr.  Rounding effects of quenched randomness on first-order phase transitions. Comm. Math. Phys. 130, 489 (1990).\\
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M. Aizenman and E.H. Lieb. Magnetic Properties of Some Itinerant Electron Systems at T > 0. Phys. Rev. Lett. 65, 1470 (1990).\\
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M. Aizenman, J.T. Chayes, L. Chayes and C.M. Newman, Discontinuity of the magnetization in one-dimensional 1/|x – y|^2 Ising and Potts models, J. Stat. Phys. 50, 1 (1988).\\
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M. Aizenman and D. Barsky.  Sharpness of the Phase Transition in Percolation Models. Comm. Math. Phys. 108, 489 (1987).\\
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M. Aizenman, H. Kesten and C. Newman.  Uniqueness of the Infinite Cluster and Continuity of Connectivity Functions for Short and Long Range Percolation. Comm. Math. Phys. 111, 505 (1987).  \\
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M. Aizenman and R. Holley. Rapid Convergence to Equilibrium of Stochastic Ising Models in the Dobrushin Shlosman Regime. In: Percolation Theory and Ergodic Theory of Infinite Particle Systems (The IMA Volumes in Math. and Its Applic.; v. 8), H. Kesten, (ed.). (Springer-Verlag 1987).\\
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M. Aizenman, D. Barsky and R. Fernández.  The Phase Transition in a General Class of Ising-Type Models is Sharp. J. State. Phys. 47, 343 (1987).\\
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M. Aizenman and C.M. Newman.  Discontinuity of the percolation density in one-dimensional 1/|x−y|^2 percolation models.  Comm. Math. Phys. 107, 611 (1986).\\
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M. Aizenman and C.M. Newman. Tree Graph Inequalities and Critical Behavior in Percolation Models. J. Stat. Phys. 36, 107 (1984).\\
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M. Aizenman, J. T. Chayes, L. Chayes, J. Fröhlich and L. Russo, On a Sharp Transition From Area Law to Perimeter Law in a System of Random Surfaces, Comm. Math Phys. 92, 19 (1983).\\
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M. Aizenman.  Geometric Analysis of φ^4 Fields and Ising Models. Comm. Math. Phys., 86, 1 (1982).\\
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M. Aizenman.  Proof of the Triviality of φ^4 Field Theory and Some Mean-Field Features of Ising Models for d > 4. Phys. Rev. Let. 47, 1 (1981).\\
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M. Aizenman and B. Simon.  Brownian motion and Harnack inequality for Schrödinger operators.  Comm. Pure. Appl. Math. 32, 209 (1982)\\
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M. Aizenman and P. A. Martin. Structure of Gibbs states of one-dimensional Coulomb systems.  Comm. Math. Phys. 78, 99 (1980).\\
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M. Aizenman. Translation invariance and instability of phase coexistence in the two-dimensional Ising system. Comm. Math. Phys. 73, 83 (1980)\\
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M. Aizenman.  On Vector Fields as Generators of Flows: A Counterexample to Nelson's Conjecture. Annals of Math. 107, 287 (1978).