Michael Aizenman   

Professor of Physics and Mathematics
Princeton University

PDF fies of recent works are available at:   arXive (search Aizenman, check Math. and Phys.)

Preprints  

(With S. Warzel) Resonant delocalization for random Schrödinger operators on tree graphs.
(http://arxiv.org/abs/1104.0969, to appear in JEMS (J. Europ. Math. Soc.))

Articles in refereed journals   (Conf. Proceedings / Reviews are listed separately)

(With 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).

(With S. Warzel) Absence of mobility edge for the Anderson random potential on tree graphs at weak disorder. Euro. Phys. Lett. 96, 37004 (2011).

(With S. Warzel) Extended States in a Lifshits Tail Regime for Random Schrödinger Operators on Trees. Phys. Rev. Lett. 106, 136801 (2011).

(With Y. Sagi, R. Pugatch, I. Almog and N. Davidson) Motional broadening in ensembles with heavy-tail frequency distribution. Phys. Rev. A 83, 043821 (2011).

(With S. Jansen, and P. Jung) Symmetry breaking in quasi-1D Coulomb systems. Ann. Henri Poincaré 11, 1453 (2010).

(With R.L. Greenblatt, and J.L. Lebowitz) On Spin Systems with Quenched Randomness: Classical and Quantum. Physica A 389 , 2902 (2010).

(With R.L. Greenblatt, and J.L. Lebowitz) Rounding of First Order Transitions in Low-Dimensional Quantum Systems with Quenched Disorder. Phys. Rev. Lett. 103, 197201 (2009).

(with S. Warzel) Localization Bounds for Multiparticle Systems. Comm. Math. Phys. 290, 903 (2009).

(with S. Warzel) On the Joint Distribution of Energy Levels of Random Schrödinger Operators. J. Phys. A: Math. Theor. 42, 045201 (2009).

(with L-P Arguin) On the Structure of Quasi-Stationary Competing Particles Systems.
Ann. Prob. 27 , 1080 (2009).

(with F. Germinet, A. Klein, and S. Warzel) On Bernoulli Decompositions for Random Variables, Concentration Bounds, and Spectral Localization.
Prob. Th. Rel. Fields. (PTRF) 143 , 219 (2009).

(with P. Jung) On the Critical Behavior at the Lower Phase Transition of the Contact Process. Latin American Jour. Prob. and Math. Stat. (ALEA). 3, 301 (2007).

(with S. Warzel) The Canopy Graph and Level Statistics for Random Operators on Trees.
Math. Phys. Anal. Geom. (MPAG), 9, 291 (2006 [app. 2007]).

(with O. Zuk, E. Domany, and I. Kanter) From Finite-System Entropy to Entropy Rate for a Hidden Markov Process. IEEE Signal Processing Letters 13,517 (2006).

(with S. Warzel) Persistence Under Weak Disorder of AC Spectra of Quasi-Periodic Schroedinger Operators on Trees Graphs. Moscow Math. J. 5, 499 (2005 [app. 2006]).

(with R. Sims and S. Warzel) Absolutely Continuous Spectra of Quantum Tree Graphs with Weak Disorder. Comm. Math. Phys. 264, 371 (2006).

(with R. Sims and S. Warzel) Stability of the Absolutely Continuous Spectrum of Random Schroedinger Operators on Tree Graphs. Prob. Th. Rel. Fields, 136, 363 (2006).

(with A. Elgart, S. Naboko, G. Stoltz, and J.H. Schenker) Moment Analysis for Localization in Random Schrödinger Operators. Inventiones Mathematicae 163, 343 (2006).

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

(with 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).

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

(with J.H. Schenker, R.M. Friedrich, and D. Hundertmark) Finite-Volume Fractional-Moment Criteria for Anderson Localization. Comm. Math. Phys. 224, 219 (2001).

(with S. Goldstein and J.L. Lebowitz) Bounded Fluctuations and Translation Symmetry Breaking in One-dimensional Particle Systems. J. Stat. Phys. 103, 601 (2001).

(with J.H. Schenker) The creation of Spectral gaps by Graph Decorations. Lett. Math. Phys. 53, 253 (2000).

(with J.H. Schenker, R.M. Friedrich, and D. Hundertmark) Constructive Fractional-moment Criteria for Localization in Random Operators. Physica A. 279, 369 (2000).

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

(with A. Burchard, C.M. Newman and D.B. Wilson) Scaling Limits for Minimal and Random Spanning Trees in Two Dimensions. Rand. Struct. Alg. 15, 319 (1999).

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

(with P. Contucci) Stability of the Quenched State in Mean Field Spin Glass Models. J. Stat. Phys. 92, 765 (1998).

(with G.M. Graf) Localization Bounds for an Electron Gas. J. Phys. A: Math. Gen. 31, 6783 (1998).

On the Number of Incipient Spanning Clusters. Nuclear Physics B [FS] 485, 551 (1997).

On the Slow Decay of O(2) Correlations in the Absence of Topological Excitations; remark on the Patrascioiu-Seiler model. J. Stat. Phys. 77, 351 (1994).

Localization at Weak Disorder: Some Elementary Bounds. Rev. Math. Phys. 6, 1163 (1994).

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

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

(with G. Grimmett) Strict Monotonicity of Critical Points in Percolation and Ferromagnetic Models. J. Stat. Phys., 63, 817 (1991).

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

(with E. H. Lieb) Magnetic Properties of Some Itinerant Electron Systems at T > 0. Phys. Rev. Lett., 65, 1470-1473 (1990).

(with J. Wehr) Rounding Effects of Quenched Randomness on First-Order Phase Transitions. Comm. Math. Phys. 130, 489 (1990).

(with J. Wehr) Fluctuations of Extensive Functions of Quenched Random Couplings. J. Stat. Phys. 60, 287 (1990).

(with J. Wehr) Rounding of First-Order Phase Transitions in Systems with Quenched Disorder. Phys. Rev. Lett., 62, 2503 (1989). Erratum: PRL, 64, 1311 (E) (1990).

(with J. Lebowitz) Metastability in Bootstrap Percolation. J. Phys. A: Math. Gen. 21, 3801 (1988).

(with R. Fernández) Critical Exponents for Long-Range Interactions. Lett. Math. Phys. 16, 39 (1988).

(with J. Bricmont and J. L. Lebowitz) Percolation of the Minority Spins in High-Dimensional Ising Models. J. Stat. Phys., 49 859, (1987).

(with J. T. Chayes, L. Chayes and C. Newman) Discontinuity of the Order Parameter in One Dimensional 1/(x-y)^2 Ising and Potts Models. J. Stat. Phys., 50 1, (1988).

(with D. Ruelle and J. L. Lebowitz) Some Rigorous Results on the Sherrington-Kirkpatrik Spin Glass Model. Comm. Math. Phys., 112 3, (1987). Addendum: CMP 116 527 (1988).

(with J. T. Chayes, L. Chayes and C. Newman) The Phase Boundary in Dilute and Random Ising and Potts Ferromagnets. J. Phys. A: Math. Gen., 20, L 313 (1987).

Rigorous Studies of Critical Behavior. Physica, 140 A, 225 (1986).

(with D. Barsky and R. Fernández) The Phase Transition in a General Class of Ising-Type Models is Sharp. J. State. Phys. 47, 343 (1987).

(with 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).

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

(with 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).

(with C. Newman) Discontinuity of the Percolation Density in One Dimensional 1/(x-y)^2 Percolation Models. Comm. Math. Phys., 107, 611 (1986).

(with R. Fernández) On the Critical Behavior of the Magnetization in High-Dimensional Ising Models. J. Stat. Phys., 44, 383 (1986).

(with M. Harn) On the Vanishing of the Surface Tension in a Random Surface Model. Nucl. Phys., B 257 [FS 14], 859 (1985).

Absence of an Intermediate Phase in a General Class of One Component Ferromagnetic Systems. Phys. Rev. Lett., 54, 839 (1985).

Self Intersection of Brownian Paths as a Case Study of a Renormalization Group Method for Quantum Field Theory. Comm. Math. Phys., 97, 91 (1985).

(with J. Fröhlich) Topological Anomalies in the n-Dependence of the n-States Potts Lattice Gauge Theory. Nucl. Phys., B 235 [FS 11], 1 (1984).

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

(with J. T. Chayes, L. Chayes, J. Fröhlich and L. Russo) On a Sharp Transition from Area Law to a Perimeter Law in a System of Random Surfaces. Comm. Math. Phys., 92, 19 (1983).

(with R. Graham) On the Renormalized Coupling Constant and the Susceptibility in φ^4 Field Theory and the Ising Model in Four Dimensions. Nucl. Phys., B 255 [FS9], 261 (1983).

(with B. Simon) Brownian Motion and Harnack Inequality for Schrödinger Operators. Commun. Pure and Appl. Math., 35, 209 (1982).

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

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).

(with E. H. Lieb) The III-rd Law of Thermodynamics and the Degeneracy of Ground States in Lattice Systems. J. Stat. Phys., 24, 279 (1981).

(with J. Fröhlich) States of One-Dimensional Coulomb Systems as Simple Examples of θ -vacua and Confinement. J. Stat. Phys., 26, 347 (1981).

(with P. A. Martin) Structure of Gibbs States of One Dimensional Coulomb Systems. Comm. Math. Phys., 78, 99 (1980).

(with B. Simon) Local Ward Identities and the Decay of Correlations in Ferromagnets. Comm. Math. Phys., 77, 137 (1980).

(with B. Simon) A Comparison of Plane Rotor and Ising Models. Phys. Lett., 76A, 281 (1980).

(with F. Delyon and B. Souillard) Lower Bounds on the Cluster Size Distribution. J. Stat. Phys., 23 267 (1980).

(with H. Spohn) Probabilistic Methods for Stationary Problems of Linear Transport Theory. J. Stat. Phys., 21, 23 (1979).

(with T. A. Bak) Convergence to Equilibrium in a System of Reacting Polymers. Comm. Math. Phys., 65, 203 (1979).

Translation Invariance and Instability of Phase Coexistence in the Two Dimensional Ising System. Comm. Math. Phys., 73, 83 (1980).

Instability of Phase Coexistence and Translation Invariance in Two Dimensions. Phys. Rev. Lett., 43, 407 (1979).

(with S. Goldstein and J. L. Lebowitz) Conditional Equilibrium and the Equivalence of Microcanonical and Grand Canonical Ensembles in the Thermodynamic Limit. Comm. Math. Phys., 62, 279 (1978).

(with E. H. Lieb) On Semi-Classical Bounds for Eigenvalues of Schrödinger Operators. Phys. Lett., 66A, 427 1978.

A Sufficient Condition for the Avoidance of Sets by Measure Preserving Flows in R^n. Duke Journal of Math., 45 809, (1978).

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

(with J. L. Lebowitz and J. Marro) Time Displaced Correlation Functions in an Infinite One Dimensional Mixture of Hard Rods with Different Diameters. J. Stat. Phys., 18, 287 (1978).

(with E. B. Davies and E. H. Lieb) Positive Linear Maps Which are Order Bounded on C* Subalgebras. Adv. in Math., 28, 84 (1978).

(with S. Goldstein, C. Gruber, J. L. Lebowitz and P. Martin) On the Equivalence Between KMS-States and Equilibrium States for Classical Systems. Comm. Math. Phys., 53, 209 (1977).

(with G. Gallavotti, S. Goldstein and J. L. Lebowitz) Stability and Equilibrium States of Infinite Classical Systems. Comm. Math. Phys., 48, 1 (1976).

(with J. L. Lebowitz and S. Goldstein) On the Stability of Equilibrium States of Finite Classical Systems. J. Math. Phys., 16, 1284 (1975).

(with S. Goldstein and J. L. Lebowitz) Ergodic Properties of an Infinite One Dimensional Hard Rod System. Comm. Math. Phys., 39, 288 (1975).

(with H. Gutfreund) Momentum Distribution in the Tomonaga Model at Finite Temperatures. J. Math. Phys., 15, 643 (1974).

Note: Conference Proceedings are listed separately (see Conf. Proceedings / Reviews).

Last updated:  4/25/2008