MAselect_Nov07

Homepage | Research Articles | Selected Works| Conf. Proceedings | Curriculum Vitae

MICHAEL AIZENMAN -- SELECTED PUBLICATIONS
and lectures

Numbers refer to the list of journal articles (#), and the list of conference proceedings/reviews ([#] ).
Recent PDf files can be downloadd from: arXive (check Math. and Phys.)

8. On Vector Fields as Generators of Flows: A Counterexample to Nelson's Conjecture. Annals of Math. 107, 287 (1978).
12. Instability of Phase Coexistence and Translation Invariance in Two Dimensions. Phys. Rev. Lett., 43, 407 (1979).
19. (with P. A. Martin) Structure of Gibbs States of One Dimensional Coulomb Systems. Comm. Math. Phys., 78, 99 (1980).
22. Proof of the Triviality of φ^4 Field Theory and Some Mean-Field Features of Ising Models for d>4. Phys. Rev. Lett., 47, 1 (1981).
23. Geometric Analysis of φ^4 Fields and Ising Models. 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).
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).
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).
35. (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. Stat. Phys. 47, 343 (1987).
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).
44. (with J. Lebowitz) Metastability in Bootstrap Percolation. J. Phys. A: Math. Gen. 21, 3801 (1988).
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, 1470-1473 (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).
53. Localization at Weak Disorder: Some Elementary Bounds. Rev. Math. Phys. 6, 1163 (1994).
55. On the Number of Incipient Spanning Clusters. Nuclear Physics B [FS] 485, 551 (1997).
[12.] 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.).
56. (with G.M. Graf) Localization Bounds for an Electron Gas. J. Phys. A: Math. Gen. 31, 6783 (1998).
58. (with A. Burchard) Hölder Regularity and Dimension Bounds for Random Curves. Duke Math. J. 99, 419 (1999).
60. (with A. Aharony and B. Duplantier) Connectivity Exponents and External Perimeter in 2D Independent Percolation Models. Phys. Rev. Lett. 83, 1359 (1999).
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, 214403 (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, 023612 (2004).
68. (with A. Elgart, S. Naboko, G. Stoltz, and J.H. Schenker) Moment Analysis for Localization in Random Schrödinger Operators. Invent. Math. 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).
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 [appeared in 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).
74. (with S. Warzel) The Canopy Graph and Level Statistics for Random Operators on Trees. Math. Phys. Anal. Geom. (MPAG), 9, 291 (2006 [appeared in 2007]).
75. (with F. Germinet, A. Klein, and S. Warzel) On Bernoulli Decompositions for Random Variables, Concentration Bounds, and Spectral Localization. Prob. Th. Rel Fields (PTRF), (PTRF) 143 , 219 (2009).
76. (with L-P Arguin) On the Structure of Quasi-Stationary Competing Particles Systems. Ann. Probab. 27 , 1080 (2009).
78. (with S. Warzel) Localization Bounds for Multiparticle Systems.
Comm. Math. Phys. 290, 903 (2009).
79. (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).