Michael Aizenman - Publications 2. I. Articles published in refereed journals

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1 Michael Aizenman - Publications 2 I. Articles published in refereed journals 1. (with H. Gutfreund) Momentum Distribution in the Tomonaga Model at Finite Temperatures. J. Math. Phys., 15, 643 (1974). 2. (with S. Goldstein and J. L. Lebowitz) Ergodic Properties of an Infinite One Dimensional Hard Rod System. Comm. Math. Phys., 39, 288 (1975). 3. (with J. L. Lebowitz and S. Goldstein) On the Stability of Equilibrium States of Finite Classical Systems. J. Math. Phys., 16, 1284 (1975). 4. (with G. Gallavotti, S. Goldstein and J. L. Lebowitz) Stability and Equilibrium States of Infinite Classical Systems. Comm. Math. Phys., 48, 1 (1976). 5. (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). 6. (with E. B. Davies and E. H. Lieb) Positive Linear Maps Which are Order Bounded on C Subalgebras. Adv. in Math., 28, 84 (1978). 7. (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). 8. On Vector Fields as Generators of Flows: A Counterexample to Nelson s Conjecture. Annals of Math. 107, 287 (1978). 9. A Sufficient Condition for the Avoidance of Sets by Measure Preserving Flows in R n. Duke Journal of Math., , (1978). 10. (with E. H. Lieb) On Semi-Classical Bounds for Eigenvalues of Schrödinger Operators. Phys. Lett., 66A, (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). 12. Instability of Phase Coexistence and Translation Invariance in Two Dimensions. Phys. Rev. Lett., 43, 407 (1979). 13. Translation Invariance and Instability of Phase Coexistence in the Two Dimensional Ising System. Comm. Math. Phys., 73, 83 (1980). 14. (with T. A. Bak) Convergence to Equilibrium in a System of Reacting Polymers. Comm. Math. Phys., 65, 203 (1979). 15. (with H. Spohn) Probabilistic Methods for Stationary Problems of Linear Transport Theory. J. Stat. Phys., 21, 23 (1979). 16. (with F. Delyon and B. Souillard) Lower Bounds on the Cluster Size Distribution. J. Stat. Phys., (1980). 17. (with B. Simon) A Comparison of Plane Rotor and Ising Models. Phys. Lett., 76A, 281 (1980).

2 Michael Aizenman - Publications (with B. Simon) Local Ward Identities and the Decay of Correlations in Ferromagnets. Comm. Math. Phys., 77, 137 (1980). 19. (with P. A. Martin) Structure of Gibbs States of One Dimensional Coulomb Systems. Comm. Math. Phys., 78, 99 (1980). 20. (with J. Fröhlich) States of One-Dimensional Coulomb Systems as Simple Examples of θ-vacua and Confinement. J. Stat. Phys., 26, 347 (1981). 21. (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). 22. 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). 23. Geometric Analysis of ϕ 4 Fields and Ising Models, Parts I & II. Comm. Math. Phys., 86, 1 (1982). 24. (with B. Simon) Brownian Motion and Harnack Inequality for Schrödinger Operators. Commun. Pure and Appl. Math., 35, 209 (1982). 25. (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). 26. (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). 27. (with C. Newman) Tree Graph Inequalities and Critical Behavior in Percolation Models. J. Stat. Phys., 36, 107 (1984). 28. (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). 29. Self Intersection of Brownian Paths as a Case Study of a Renormalization Group Method for Quantum Field Theory. Comm. Math. Phys., 97, 91 (1985). 30. Absence of an Intermediate Phase in a General Class of One Component Ferromagnetic Systems. Phys. Rev. Lett., 54, 839 (1985). 31. (with M. Harn) On the Vanishing of the Surface Tension in a Random Surface Model. Nucl. Phys., B 257 [FS 14], 859 (1985). 32. (with R. Fernández) On the Critical Behavior of the Magnetization in High-Dimensional Ising Models. J. Stat. Phys., 44, 383 (1986). 33. (with C. Newman) Discontinuity of the Percolation Density in One Dimensional 1/(x y) 2 Percolation Models. Comm. Math. Phys., 107, 611 (1986). 34. (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).

3 Michael Aizenman - Publications (with D. Barsky) Sharpness of the Phase Transition in Percolation Models. Comm. Math. Phys., 108, 489 (1987). 36. (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). 37. (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). 38. Rigorous Studies of Critical Behavior. Physica, 140 A, 225 (1986). 39. (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). 40. (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 (1988). 41. (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). 42. (with J. Bricmont and J. L. Lebowitz) Percolation of the Minority Spins in High-Dimensional Ising Models. J. Stat. Phys., , (1987). 43. (with R. Fernández) Critical Exponents for Long-Range Interactions. Lett. Math. Phys. 16, 39 (1988). 44. (with J. Lebowitz) Metastability in Bootstrap Percolation. J. Phys. A: Math. Gen. 21, 3801 (1988). 45. (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). 46. (with J. Wehr) Fluctuations of Extensive Functions of Quenched Random Couplings. J. Stat. Phys. 60, 287 (1990). 47. (with J. Wehr) Rounding Effects of Quenched Randomness on First-Order Phase Transitions. Comm. Math. Phys. 130, 489 (1990). 48. (with E. H. Lieb) Magnetic Properties of Some Itinerant Electron Systems at T > 0. Phys. Rev. Lett., 65, (1990). 49. (with D. Barsky) Percolation Critical Exponents Under the Triangle Condition. Ann. Prob. 13, 1520 (1991). 50. (with G. Grimmett) Strict Monotonicity of Critical Points in Percolation and Ferromagnetic Models. J. Stat. Phys., 63, 817 (1991). 51. (with S. Molchanov) Localization at Large Disorder and at Extreme Energies: an Elementary Derivation. Comm. Math. Phys. 157, 245 (1993). 52. (with B. Nachtergaele) Geometric Aspects of Quantum Spin States. Comm. Math. Phys. 164, 17 (1994).

4 Michael Aizenman - Publications Localization at Weak Disorder: Some Elementary Bounds. Rev. Math. Phys. 6, 1163 (1994). 54. 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). 55. On the Number of Incipient Spanning Clusters. Nuclear Physics B [FS] 485, 551 (1997). 56. (with G.M. Graf) Localization Bounds for an Electron Gas. J. Phys. A: Math. Gen. 31, 6783 (1998). 57. (with P. Contucci) Stability of the Quenched State in Mean Field Spin Glass Models. J. Stat. Phys. 92, 765 (1998). 58. (with A. Burchard) Hölder Regularity and Dimension Bounds for Random Curves. Duke Math. J. 99, 419 (1999). 59. (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). 60. (with A. Aharony and B. Duplantier) Connectivity Exponents and External Perimeter in 2D Independent Percolation Models. Phys. Rev. Lett. 83, 1359 (1999). 61. (with J.H. Schenker, R.M. Friedrich, and D. Hundertmark) Constructive Fractionalmoment Criteria for Localization in Random Operators. Physica A. 279, 369 (2000). 62. (with J.H. Schenker) The creation of Spectral gaps by Graph Decorations. Lett. Math. Phys. 53, 253 (2000). 63. (with S. Goldstein and J.L. Lebowitz) Bounded Fluctuations and Translation Symmetry Breaking in One-dimensional Particle Systems. J. Stat. Phys. 103, 601 (2001). 64. (with J.H. Schenker, R.M. Friedrich, and D. Hundertmark) Finite-Volume Fractional- Moment Criteria for Anderson Localization. Comm. Math. Phys. 224, 219 (2001). 65. (with R. Sims, and S.L. Starr) Extended variational principle for the Sherrington-Kirkpatrick spin-glass model. Phys. Rev. B 68, (2003). 66. (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, (2004). 67. (with A. Ruzmaikina) Characterization of Invariant Measures at the Leading Edge for Competing Particle Systems. Ann. Probab., 33, 82, (2005). 68. (with A. Elgart, S. Naboko, G. Stoltz, and J.H. Schenker) Moment Analysis for Localization in Random Schrödinger Operators. Inventiones Mathematicae 163, 343 (2006). 69. (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). 70. (with R. Sims and S. Warzel) Absolutely Continuous Spectra of Quantum Tree Graphs with Weak Disorder. Comm. Math. Phys. 264, 371 (2006). 71. (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]).

5 Michael Aizenman - Publications (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). 73. (with S. Warzel) The Canopy Graph and Level Statistics for Random Operators on Trees. Math. Phys. Anal. Geom. (MPAG), 9, 291 (2006 [app. 2007]). Submitted for publication 74. (with P. Jung) On the Critical Behavior at the Lower Phase Transition of the Contact Process. To appear in Latin American Jour. Prob. and Math. Stat. (ALEA). 75. (with F. Germinet, A. Klein, and S. Warzel) On Bernoulli Decompositions for Random Variables, Concentration Bounds, and Spectral Localization (preprint 2007). 76. (with L-P Arguin) On the Structure of Quasi-Stationary Competing Particles Systems.

6 Michael Aizenman - conference proceedings 7 II. Conference Proceedings and Refereed Compilations 1. (with S. Goldstein and J. L. Lebowitz) Ergodic Properties of Infinite Systems. In: Dynamical Systems, Proceedings of the Fifth Battelle Rencontres, 1974, Lecture Notes, Springer-Verlag (1975). 2. On Extension of Flows in the Presence of Sets of Singularities. In: Mathematical Problems in Theoretical Physics (Proceedings, Rome 1977), Lecture Notes in Physics, Vol. 80, Springer-Verlag (1978). 3. Instability of Phase Coexistence and Translation Invariance in Two Dimensions. In: Mathematical Problems in Theoretical Physics (Proceedings, Lausanne 1979), K. Osterwalder, ed., Lecture Notes in Physics, 116, Springer-Verlag, Internal Structure of Coulomb Systems in One-Dimension. In: Rigorous Atomic and Molecular Physics, NATO Advanced Study Institute Series, Series B: Physics 74, G. Velo and A. S. Wightman (eds.), Plenum Press, New York and London, Geometric Analysis of ϕ 4 Fields and Ising Models. In: Mathematical Problems in Theoretical Physics (Proceedings, Berlin 1981), R. Schrader, (ed.). Lecture Notes in Physics, 153, Springer-Verlag, Rigorous Results on the Critical Behavior in Statistical Mechanics. In: Scaling and Self Similarity (Renormalization in Statistical Mechanics and Dynamics), J. Fröhlich, (ed.). Birkhäuser (Boston, 1983). 7. Rigorous Studies of Critical Behavior. In: Applications of Field Theory in Statistical Mechanics (Proceedings Sitges 1984), L. Garrido (ed.). Springer-Verlag Lecture Notes in Physics Rigorous Studies of Critical Behavior II. In: Statistical Physics and Dynamical Systems, Rigorous Results, J. Fritz, A. Jaffe and D. Szäsz, (eds.). Birkhäuser, (Boston-Basel- Stuttgart, 1985). 9. General Results in Percolation Theory. In: Proceedings of the Taniguchi Workshop and Symposium on Probabilistic Methods in Mathematical Physics, Katata and Kyoto 1985, N. Ikeda, (ed.). (Academic Press, 1987). 10. (with A. Klein and C.M. Newman) Percolation Methods for Disordered Quantum Ising Models. In: Phase Transitions: Mathematics, Physics, Biology..., (ed.). R. Kotecky, World Scientific (Singapore, 1993). 11. The Geometry of Critical Percolation and Conformal Invariance. In: Proceedings STAT- PHYS19 (Xiamen 1995), H. Bai-lin (ed.), World Scientific Scaling Limit for the Incipient Spanning Clusters. In Mathematics of Multiscale Materials. Editors: K.M. Golden, G.R. Grimmett, R.D. James, and P.N. Sen, The IMA Volumes in Mathematics and its Applications (Springer, 1998.). 13. (with A. Elgart, S. Naboko, J.H. Schenker, G. Stolz) Fractional Moment Methods for Anderson Localization in the Continuum, Proceedings, 14th Int. Cong. Math. Phys. (Lisbon 2003), J.-C. Zambrini (ed.), (World Scientific, 2006).

7 Michael Aizenman - conference proceedings (with E.H. Lieb, R. Seiringer, J.P. Solovej, and J. Yngvason) Bose-Einstein Condensation as a Quantum Phase Transition in an Optical Lattice, in Mathematical Physics of Quantum Mechanics (Proceedings QMath9, Giens 2004). Springer Lecture Notes in Physics, Vol. 690, J. Asch and A. Joye (eds.), (Springer, 2006). 15. (with R. Sims and S. Warzel: Fluctuation Based Proof of the Stability of AC Spectra of Random Operators on Tree Graphs. In Quantum Graphs and Their Applications, (Proceedings AMS-IMA-SIAM Joint Res. Conf., Snowbird 2005). G. Berkolaiko, R. Carlson, S.A. Fulling, and P. Kuchment (eds.). AMS Contemporary Mathematics Series, vol. 415 (AMS, 2006). 16. (with R. Sims and S. L. Starr) Mean-Field Spin Glass models from the Cavity ROSt Perspective. In Prospects in Mathematical Physics (Proceedings Young Res. Symp. ). J.C. Mourão, J.P. Nunes, R. Picken, and J-C Zambrini (eds.) AMS Contemporary Mathematics Series, vol. 437 (AMS, 2007). 17. Perspectives in Statistical Mechanics. In Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon s 60th Birthday, F. Gesztesy, P. Deift, C. Galvez, P. Perry, W. Schlag (eds.) Proceedings of Symposia in Pure Mathematics, vol (AMS, 2007). Note: articles in regular refereed journals are listed separately (see above). Books Edited ). The State of Matter. Co-edited with H. Araki, World-Scientific (Singapore,