Michael Aizenman - Selected Publications#

M. Aizenman, S. Warzel. Random Operators: Disorder Effects on Quantum Spectra and Dynamics (Grad. Studies in Mathematics, AMS 2015).

M. Aizenman, S. Warzel: A Boosted Simon-Wolff Spectral Criterion and Resonant Delocalization. Commun. Pure Appl. Math. (2015) doi:10.1002/cpa.21625.

M. Aizenman, H. Duminil-Copin and V. Sidoravicius) Random Currents and Continuity of Ising Model’s Spontaneous Magnetization, Comm. Math. Phys. 334, 719 (2015).

M. Aizenman, S. Warzel: On the ubiquity of the Cauchy distribution in spectral problems, Probab. Theory Relat. Fields 163, 61 (2015).

M. Aizenman and S. Warzel. Resonant delocalization for random Schrödinger operators on tree graphs, J. Euro. Math. Soc. 15, 1167 (2013).

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).

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).

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).

A. Ruzmaikina and M. Aizenman. Characterization of Invariant Measures at the Leading Edge for Competing Particle Systems. Ann. Probab. 33, 82, (2005).

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).

M. Aizenman, R. Sims and S.L. Starr. Extended variational principle for the Sherrington-Kirkpatrick spin-glass model. Phys. Rev. B 68, 214403 (2003).

M. Aizenman and A. Burchard. Hölder Regularity and Dimension Bounds for Random Curves. Duke Math. J. 99, 419 (1999).

M. Aizenman, A. Aharony and B. Duplantier. Connectivity Exponents and External Perimeter in 2D Independent Percolation Models. Phys. Rev. Lett. 83, 1359 (1999).

M. Aizenman and B. Nachtergaele. Geometric Aspects of Quantum Spin States. Comm. Math. Phys. 164, 17 (1994).

M. Aizenman and S. Molchanov. Localization at Large Disorder and at Extreme Energies: an Elementary Derivation. Comm. Math. Phys. 157, 245 (1993).

D. Barsky and M. Aizenman. Percolation Critical Exponents Under the Triangle Condition. Ann. Prob. 13, 1520 (1991).

M. Aizenman and J. Wehr. Rounding effects of quenched randomness on first-order phase transitions. Comm. Math. Phys. 130, 489 (1990).

M. Aizenman and E.H. Lieb. Magnetic Properties of Some Itinerant Electron Systems at T > 0. Phys. Rev. Lett. 65, 1470 (1990).

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).

M. Aizenman and D. Barsky. Sharpness of the Phase Transition in Percolation Models. Comm. Math. Phys. 108, 489 (1987).

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).

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).

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).

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).

M. Aizenman and C.M. Newman. Tree Graph Inequalities and Critical Behavior in Percolation Models. J. Stat. Phys. 36, 107 (1984).

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).

M. Aizenman. Geometric Analysis of φ^4 Fields and Ising Models. Comm. Math. Phys., 86, 1 (1982).

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).

M. Aizenman and B. Simon. Brownian motion and Harnack inequality for Schrödinger operators. Comm. Pure. Appl. Math. 32, 209 (1982)

M. Aizenman and P. A. Martin. Structure of Gibbs states of one-dimensional Coulomb systems. Comm. Math. Phys. 78, 99 (1980).

M. Aizenman. Translation invariance and instability of phase coexistence in the two-dimensional Ising system. Comm. Math. Phys. 73, 83 (1980)

M. Aizenman. On Vector Fields as Generators of Flows: A Counterexample to Nelson's Conjecture. Annals of Math. 107, 287 (1978).