Lectures on Logarithmic Sobolev Inequalities

A. Guionnet; B. Zegarlinski

Séminaire de probabilités de Strasbourg (2002)

  • Volume: 36, page 1-134

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Guionnet, A., and Zegarlinski, B.. "Lectures on Logarithmic Sobolev Inequalities." Séminaire de probabilités de Strasbourg 36 (2002): 1-134. <http://eudml.org/doc/114087>.

@article{Guionnet2002,
author = {Guionnet, A., Zegarlinski, B.},
journal = {Séminaire de probabilités de Strasbourg},
language = {eng},
pages = {1-134},
publisher = {Springer - Lecture Notes in Mathematics},
title = {Lectures on Logarithmic Sobolev Inequalities},
url = {http://eudml.org/doc/114087},
volume = {36},
year = {2002},
}

TY - JOUR
AU - Guionnet, A.
AU - Zegarlinski, B.
TI - Lectures on Logarithmic Sobolev Inequalities
JO - Séminaire de probabilités de Strasbourg
PY - 2002
PB - Springer - Lecture Notes in Mathematics
VL - 36
SP - 1
EP - 134
LA - eng
UR - http://eudml.org/doc/114087
ER -

References

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  1. [1] Aida, S.; Stroock, D.W.; Moment estimates derived from Poincaré and logarithmic Sobolev inequalities. Math.Res.Lett.1, No. 1, 75-86 (1994) Zbl0862.60064MR1258492
  2. [2] Aizenmann, M.; Holley, R.; Rapid Convergence to Equilibrium of Stochastic Ising Models in the Dobrushin-Shlosman Regime, Percolation Theory and Ergodic Theory of Infinite Particle Systems, ed. Kesten H, Springer-Verlag, 1-11 (1987) Zbl0621.60118MR894538
  3. [3] Albeverio, S.; Kondratiev Yu.G. ; Röckner, M.; Dirichlet operators and Gibbs measures, Collection: On Klauder's path: a field trip, World Sci. Publishing, River Edge, NJ, 1-10, (1994) Zbl0943.31500MR1350556
  4. [4] Albeverio, S.; Röckner, M.; Dirichlet Form Methods for Uniqueness of Martingale Problems and Applications Collection: Stochastic analysis (Ithaca, NY, 1993), 513-528Proc. Sympos. Pure Math.57, Amer. Math. Soc., Providence, RI (1995) Zbl0824.31005MR1335494
  5. [5] Bakry, D.; L'Hypercontractivité et son Utilisation en Théorie des Semi-Groupes, Lectures on Probability Theory, Ecole d'Eté de Probabilités de Saint-Flour XXII - 1992, Ed. P. Bernard, LNM1581, 1-114 (1994) Zbl0856.47026MR1307413
  6. [6] Bakry, D.; Emery, M.; Diffusions Hypercontractives, Séminaire de Probabilités XIX (1983/84 Proceedings), LNM1123 (Eds J. Azéma and M. Yor), 177-206 (1985) Zbl0561.60080MR889476
  7. [7] Bakry, D. and Ledoux, M.; Lévy-Gromov Isoperimetric Inequality for an Infinite Dimensional Diffusion Generator, Invent. Math.123, 259-281 (1996). Zbl0855.58011MR1374200
  8. [8] Beckner, W.; Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality, Ann. of Math.138, 213 - 242 (1993) Zbl0826.58042MR1230930
  9. [9] Bertini, L.; Zegarlinski, B.; Coercive inequalities for Gibbs measure. J. Funct. Anal.162, no 2, 257-286 (1999) Zbl0932.60061MR1682059
  10. [10] Bobkov, S.G.; An Isoperimetric Inequality on the Discrete Cube, And an Elementary Proof of the Isoperimetric Inequality in Gauss Space, Ann. Prob.25, 206 - 214 (1997) Zbl0883.60031MR1428506
  11. [11] Bobkov, S.G.; Gotze, F. ; Exponential integrability and transportation cost related to log-Sobolev inequalities. J. Funct. Anal.163, no 1, 1-28 (1999) Zbl0924.46027MR1682772
  12. [12] Bourbaki, N.; Théories Spectrales, Hermann (1967) Zbl0152.32603
  13. [13] Carlen, E.A.; Stroock, D.W.; An application of the Bakry-Emery criterion to infinite dimensional diffusions, Sém. de Probabilités XX, Azéma J. and Yor M. (eds.) LNM1204, 341-348 (1986) Zbl0609.60086MR942029
  14. [14] Cesi, F.; Maes, C.; Martinelli, F.; Relaxation of disordered magnets in the Griffiths regime. Commun. Math. Phys.188, no 1, 135-173 (1997) Zbl0882.60095MR1471335
  15. [15] Cesi, F.; Maes, C.; Martinelli, F.; Relaxation to equilibrium for two dimensional disordered Ising systems in the Griffiths phase. Commun. Math. Phys.189, No 2, 323-335 (1997) Zbl0888.60090MR1480022
  16. [16] Chen, M.; Wang, F.; Estimates of logarithmic Sobolev constant: An improvement of Bakry-Emery criterion. J. Funct. Anal.144, no.2, 287-300 (1997) Zbl0872.58066MR1432586
  17. [17] Chung, F.K.; GRIGOR'YAN, A.; Yau, S.T. ; Eigenvalues and a diameter for manifolds and graphs. Tsing Hua lectures on geometry and analysisTaiwan (1990-91), International press, 79-105 (1997) Zbl0890.58093MR1482032
  18. [18] Davies, E.B.; Heat kernels and spectral theory, Cambridge University Press (1989) Zbl0699.35006MR990239
  19. [19] Davies, E.B.; Gross L.; Simon, B.; Hypercontractivity : A bibliographical review, Proceedings of the Hoegh-Krohn Memorial Conference, Eds. S. Albeverio, J.E. Fenstad, H. Holden and T. Lindstrom, 370-389. Zbl0790.46055MR1190534
  20. [20] Davies, E.B.; Simon, B.; Ultracontractivity and the Heat Kernel for Schrödinger Operators and Dirichlet Laplacians, J. Func. Anal.59, 335-395 (1984) Zbl0568.47034MR766493
  21. [21] Deuschel, J.-D.; Algebraic L2 Decay of Attractive Critical Processes on the Lattice, Ann. Prob.22, 264-283 (1994) Zbl0811.60089MR1258877
  22. [22] Deuschel, J.-D.; Stroock, D.W.; Large deviations, Academic Press Inc. (1989) Zbl0705.60029MR997938
  23. [23] Deuschel, J.-D.; Stroock, D.W.; Hypercontractivity and Spectral Gap of Symmetric Diffusions with applications to the Stochastic Ising Model, J. Func. Anal.92, 30-48 (1990) Zbl0705.60066MR1064685
  24. [24] Diaconis, P.; Saloff-Coste, L.; Nash inequalities for finite Markov chains, J. Theor. Probab.9, no 2, 459-510 (1996) Zbl0870.60064MR1385408
  25. [25] Diaconis, P.; Saloff-Coste, L.; Logarithmic Sobolev inequalities for finite Markov chains, Ann. Appl. Probab.6, no 3, 695-750 (1996) Zbl0867.60043MR1410112
  26. [26] Dobrushin, R.; The description of Random Fields by Means of Conditional Probabilities and Conditions of its Regularity, Theor. Prob. its Appl.13, 197-224 (1968) Zbl0184.40403
  27. [27] Dobrushin, R.; Prescribing a system of random variables by conditionnal distribution, Theor. prob. Appl.15, 458-486 (1970) Zbl0264.60037
  28. [28] Dobrushin, R.; Markov Processes with a Large Number of Locally Interacting Components Problems, Inf. Trans.7, 149-164 and 235-241 (1971) 
  29. [29] Dobrushin, R.; Kassalygo, L.A.; Uniqueness of a Gibbs Fields with Random Potential - An Elementary Approach, Theory. Probab. Appl.31, 572-589 (1986) Zbl0635.60107MR881577
  30. [30] Dobrushin, R.; Kotecky, R.; Shlosman, S.; Wulff construction. A global shape from local interaction, AMS Translations of mathematical monographs (1992) Zbl0917.60103MR1181197
  31. [31] Dobrushin, R.; Shlosman, S.; Constructive criterion for the uniqueness of Gibbs field. Statistical Physics and Dynamical Systems, Rigorous Results Eds. Fritz, Jaffe and Szasz, 347-370, Birkhäuser (1985) Zbl0569.46042MR821306
  32. [32] Dobrushin, R.; Shlosman, S.; Completely analytical Gibbs fields, Statistical Physics and Dynamical Systems, Rigorous Results Eds. Fritz, Jaffe and Szasz, 371-403, Birkhäuser (1985) Zbl0569.46043MR821307
  33. [33] Dobrushin, R.; Shlosman, S.; Completely analytical interactions: constructive description, J. Stat. Phys.46, 983-1014 (1987) Zbl0683.60080MR893129
  34. [34] Von Dreyfus, H. ; Klein, A.; Perez, J.F.; Taming Griffiths singularities : Infinite differentiability of quenched correlation functions, Comm. Math. Phys.170, 21-39 (1995) Zbl0820.60086MR1331689
  35. [35] Driver, B.; Lohrenz, T.; Logarithmic Sobolev inequalities for pinned loop groups, J. Funct. Anal.140, no 2, 381-448 (1996) Zbl0859.22012MR1409043
  36. [36] Dunlop, F.; Correlation Inequalities for multicomponent Rotators, Commun. Math. Phys., 49, 247-256 (1976) MR413945
  37. [37] Ethier, S.N.; Kurtz, T.G.; Markov Processes, characterization and convergence, J. Wiley and Sons (1985) Zbl0592.60049MR838085
  38. [38] Van Enter, A.C.D.; Zegarlinski, B. ; A Remark on Differentiability of the Pressure Functional, Rev. Math. Phys.17, 959-977 (1995) Zbl0831.60112MR1348831
  39. [39] Federbush, I.; A partially alternative derivation of a result of Nelson, J. Math. Phys10, 50-52 (1969) Zbl0165.58301
  40. [40] Fisher, D.; Huse, D.; Dynamics of droplet fluctuations in pure and random Ising systems, Phys. Rev.35, 6841 (1987) 
  41. [41] Föllmer, H.; A covariance estimate for Gibbs measures, J. Func. Anal.46, 387-395 (1982) Zbl0482.60052MR661878
  42. [42] Fougères, P.; Hypercontractivité et isopérimétrie gaussienne. Applications aux systèmes de spins., Ann. Inst. Henri Poincaré, Probabilités et Statistiques36, no 5, 647-689 (2000) Zbl0983.60097MR1792659
  43. [43] Fröhlich, J.; Imbrie, J.Z.; Improved Perturbation Expansion for Disordered Systems: Beating Griffiths Singularities. Commun. Math. Phys.96145-180 (1984) Zbl0574.60098MR768253
  44. [44] Fukushima, M.; Oshima, Y.; Takeda, M.; Dirichlet forms and symmetric Markov processes. de Gruyter Studies in Mathematics19, Walter de Gruyter and Co., Berlin, (1994) Zbl0838.31001MR1303354
  45. [45] Georgii, H.O.; Gibbs measures and phase transitions, Walter de Gruyter (1988) Zbl0657.60122MR956646
  46. [46] Gielis, G. ; PhD Thesis, Leuven (1995) 
  47. [47] Gielis, G.; Maes, C.; The uniqueness regime of Gibbs fields with unbounded disorder, J. Statist. Phys.81, no. 3-4, 829-835 (1995) Zbl1081.82519MR1359208
  48. [48] Glimm, J.; Jaffe, A.; Quantum Physics: A Functional Integral Point of View, Springer-Verlag1981, 1987 Zbl0461.46051
  49. [49] Goldstein, J.A.; Semigroups of linear operators and Applications, Oxford Science Publications (1970) 
  50. [50] Goldstein, J.A.; Ruiz Goldstein, G.; Semigroups of linear and non linear operators and Applications, Proceedings of the Curucao conference, August 1992. Kluwer Academic publishers. Zbl1107.47304MR1270689
  51. [51] Gray, L.; Griffeath, D.; On the Uniqueness of Certain Interacting Particle Systems, Z. Wahr. v. Geb.35, 75-86 (1976) Zbl0316.60067MR405643
  52. [52] Gross, L.; Logarithmic Sobolev inequalities, Amer. J. Math.97 , 1061-1083 (1976) Zbl0318.46049MR420249
  53. [53] Guionnet, A.; Zegarlinski, B.; Decay to Equilibrium in Random Spin Systems on a Lattice. Commun. Math. Phys.181, no 3, 703-732 (1996) Zbl0882.60093MR1414307
  54. [54] Guionnet, A.; Zegarlinski, B.; Decay to Equilibrium in Random Spin Systems on a Lattice. Journal of Stat.86, 899-904 (1997) Zbl0935.82039MR1438973
  55. [55] Hebey, E.; Sobolev spaces on Riemannian manifolds, LNM1635, Springer-Verlag (1996) Zbl0866.58068MR1481970
  56. [56] Herbst, I.; On Canonical Quantum Field Theories, J. Math. Phys.17, 1210-1221 (1976) MR408585
  57. [57] Higuchi, Y.; Yoshida, N.; Slow relaxation of stochastic Ising models with random and non random boundary conditions, New trends in stochastic analysis, ed. K. Elworthy, S. Kusuoka, I. Shigekawa, 153-167 (1997) MR1654356
  58. [58] Holley, R.; The one-dimensional stochastic X-Y model. Collection: Random walks, Brownian motion, and interacting particle systems, Progr. Probab.28, Birkhäuser, Boston MA, 295-307 (1991) Zbl0747.60095MR1146454
  59. [59] Holley, R.; Stroock, D.W.; Logarithmic Sobolev inequalities and stochastic Ising models.J. Stat. Phys.46, 1159-1194 (1987) Zbl0682.60109MR893137
  60. [60] Holley, R.; Stroock, D.W., Uniform and L2 Convergence in One Dimensional Stochastic Ising models, Commun. Math. Phys.123, 85-93 (1989) Zbl0666.60104MR1002033
  61. [61] Karatzas, I.; Shreve, S.E.; Brownian motion and stochastic calculus. Second edition. Graduate texts in Mathematics. Springer-Verlag. Zbl0734.60060MR1121940
  62. [62] Kunita, H.; Absolute continuity of Markov processes and generatorsNagoya Math. J.36, 1-26 (1969) Zbl0186.51203MR250387
  63. [63] Kesten, H.; Aspect of first passage percolation.Ecole d'été de St-Flour, LNM1180, 125-264 (1986) Zbl0602.60098MR876084
  64. [64] Laroche, E.; Hypercontractivité pour des systèmes de spins de portée infinie, Prob. Theo. Rel. Fields101, No. 1, 89-132 (1995) Zbl0820.60082MR1314176
  65. [65] Latala, R. and Oleszkiewicz, K.; Between Sobolev and Poincare, in Geometric Aspects of Functional Analysis, pp. 147-168, Lecture Notes in Math.1745, Springer, Berlin2000 Zbl0986.60017MR1796718
  66. [66] Ledoux, M.; Concentration of measure and logarithmic Sobolev inequalities, Sém. de Proba.33 (1997) Lecture Notes in Mathematics1709, 120-216Springer (1999) Zbl0957.60016MR1767995
  67. [67] Liggett, T.M.; Infinite Particle Systems, Springer-Verlag, Grundlehren Series 276, New York (1985) Zbl0559.60078
  68. [68] Liggett, T.M.; L2 Rates of Convergence for Attractive Reversible Nearest Particle Systems: The Critical Case, Ann. Probab.19, 935-959 (1991) Zbl0737.60092MR1112402
  69. [69] Lu, S.-L. ; Yau, H.-T.; Spectral Gap and Logarithmic Sobolev Inequality for Kawasaki and Glauber Dynamics, Commun. Math. Phys.156, 399-433 (1993) Zbl0779.60078MR1233852
  70. [70] Ma, Z.M. ; , Röckner, M. ; Introduction to the theory of (nonsymmetric) Dirichlet forms. Universitext. Springer-Verlag, Berlin (1992) Zbl0826.31001MR1214375
  71. [71] Maes, C.; Shlosman, S.; Ergodicity of probabilistic cellular automata: a constructive criterion. Comm. Math. Phys.135, no. 2, 233-251 (1991) Zbl0717.68073MR1087383
  72. [72] Maes, C.; Shlosman, S.; When is an interacting particle system ergodic?, Comm. Math. Phys.151, no. 3, 447-466 (1993) Zbl0765.60102MR1207259
  73. [73] Martinelli, F.; On the two dimensionnal dynamical Ising model in the phase coexistence region. Journal Stat. Phys.76, 1179 (1994) Zbl0839.60087MR1298100
  74. [74] Martinelli, F.; Lectures on Glauber dynamics for discrete spin modelsLectures on probability theory and statisticsLNM1717, 93-191 (St-Flour, 1997) Springer-Verlag (1999) Zbl1051.82514MR1746301
  75. [75] Martinelli, F.; Olivieri, E.; Approach to Equilibrium of Glauber Dynamics in the One Phase Region: I. The Attractive case/ II. The General Case. Commun. Math. Phys.161, 447-486 / 487-514 (1994) Zbl0793.60111MR1269387
  76. [76] Minlos, R.A.; Invariant subspaces of the stochastic Ising high temperature dynamics, Markov Process and Rel. Fields2, no. 2, 263-284 (1996) Zbl0902.60053MR1414120
  77. [77] Olivieri, E.; Picco, P.; Cluster Expansion for D-dimensional Lattice Systems and Finite Volume Factorization Properties, J. Stat. Phys.59, 221 (1990) Zbl1083.82509MR1049968
  78. [78] Olkiewicz, R.; Zegarlinski, B.; Hypercontractivity in Non-commutative Lp spaces, J. Funct. Anal.161 , 246-285 (1999) Zbl0923.46066MR1670230
  79. [79] Prakash, C.; High-temperature differentiability of lattice Gibbs states by Dobrushin uniqueness techniques, J. Stat. Phys.31, 169-228 (1983) MR711476
  80. [80] Preston, C.; Random fields, LNM534 , Springer1976 Zbl0335.60074MR448630
  81. [81] Rao, M.M. and Ren, Z.D.; Theory of Orlicz spaces , New York : Marcel Dekker, 1991 Zbl0724.46032MR1113700
  82. [82] Revuz, D.; Yor, M. ; Continuous martingales and Brownian motion. SpringerNew York (1991) Zbl0731.60002MR1083357
  83. [83] Röckner, M.; Dirichlet forms on infinite-dimensional state space and applications. Collection: Stochastic analysis and related topics (Silivri, 1990), 131-185Progr. Probab.31, Birkhäuser, Boston, MA (1992) Zbl0796.31006MR1203374
  84. [84] Reed, J.; Simon, B.; Methods of Modern Mathematical Physics , Academic Press1975 Zbl0308.47002
  85. [85] Rosen, J.; Sobolev Inequalities for Weight Spaces and Supercontractivity, Trans. A.M.S.222, 367-376 (1976) Zbl0344.46072MR425601
  86. [86] Roth, J.P. ; Opérateurs dissipatifs et semi-groupes dans les espaces de fonctions continues. Ann. Inst. Fourier26 , 1-97 (1976) Zbl0331.47021MR448158
  87. [87] Rothaus, O.S. ; Logarithmic Sobolev Inequalities and the Spectrum of Schrödinger Operators, J. Func. Anal.42, 110-378 (1981) Zbl0471.58025MR620582
  88. [88] G. Royer; Une initiation aux inégalités de Sobolev logarithmiques, Société Mathématique de France, Cours spécialisés (1999) Zbl0927.60006MR1704288
  89. [89] W. Rudin; Real and Complex AnalysisMc Graw-Hill International Zbl0142.01701
  90. [90] Ruelle D.; Statistical Mechanics: Rigorous Results. W.A. Benjamin Inc. (1969) Zbl0177.57301MR289084
  91. [91] Saloff Coste, L.; Lecture notes on finite Markov Chains, LNM1665, 301-413Springer (1997) Zbl0885.60061MR1490046
  92. [92] Schonmann, R.; Schlosman, S.; Complete analyticity for 2D Ising model completedComm. Math. Phys170, 453 (1995) Zbl0821.60097MR1334405
  93. [93] Simon B.; The P(φ)2 Euclidian (Quantum) Field Theory, Princeton Univ. Press1974 
  94. [94] Simon, B.; The Statistical Mechanics of Lattice Gasses, Princeton Univ. Press (1993) Zbl0804.60093MR1239893
  95. [95] Simon, B.; A remark on Nelson's best hypercontractive estimates, Proc. A.M.S.55, 376-378 (1976) Zbl0441.46026MR400995
  96. [96] Sinai, Y.G.; Theory of Phase Transitions : Rigorous Results, Pergamon Press, Oxford (1982) Zbl0537.60097MR691854
  97. [97] Stroock, D.W.; Logarithmic Sobolev Inequalities for Gibbs states, Dirichlet Forms, Varenna1992, LNM1563, 194-228 (Springer-Verlag993) eds G. Dell'Antonio, U. Mosco. (1993) Zbl0801.60056MR1292280
  98. [98] Stroock D.W.; Zegarlinski B.; The Logarithmic Sobolev Inequality for Continuous Spin Systems on a Lattice. J. Funct. Anal.104, 299-326 (1992) Zbl0794.46025MR1153990
  99. [99] Stroock D.W.; Zegarlinski B.; The Equivalence of the Logarithmic Sobolev Inequality and the Dobrushin-Shlosman Mixing Condition. Commun. Math. Phys.144, 303-323 (1992) Zbl0745.60104MR1152374
  100. [100] Stroock D.W.; Zegarlinski B.; The Logarithmic Sobolev inequality for Discrete Spin Systems on a Lattice. Commun. Math. Phys.149, 175-193 (1992) Zbl0758.60070MR1182416
  101. [101] Stroock D.W.; Zegarlinski B.; On the ergodic properties of Glauber dynamics. J. Stat. Phys.81, 1007-1019 (1995) Zbl1081.60562MR1361304
  102. [102] Stroock D.W.; Varadhan, S.R.S.; Diffusion processes with continuous coefficients, I and II. Comm. Pure Applied Math.22, 345-400, 479-530 (1969) Zbl0175.44802
  103. [103] Sullivan W.G.; A unified Existence and Ergodic Theorem for Markov Evolution of Random Fields, Z. Wahr. Verv. Geb.31, 47-56 (1974) Zbl0285.60058MR375534
  104. [104] Thomas L.E.; Bound on the Mass Gap for Finite Volume Stochastic Ising Models at Low Temperature. Commun. Math. Phys.126, 1-11 (1989) Zbl0679.60102MR1027910
  105. [105] Wang F.Y.; Estimates of logarithmic Sobolev constant for finite-volume continuous spin systems. J. Stat. Phys.84, No. 1-2, 277-293 (1996) Zbl1081.82534MR1401258
  106. [106] Yau H.T.; Logarithmic Sobolev inequality for lattice gases with mixing conditions. Comm. Math. Phys.181, no. 2, 367-408 (1996) Zbl0864.60079MR1414837
  107. [107] Yau H.T.; Logarithmic Sobolev inequality for generalized simple exclusion processes. Probab. Theory Related Fields109, no. 4, 507-538 (1997) Zbl0903.60087MR1483598
  108. [108] Yoshida, N.; Relaxed criteria of the Dobrushin-Shlosman mixing condition. J. Stat. Phys.87, no. 1-2, 293-309 (1997) Zbl0920.60086MR1453741
  109. [109] Zegarlinski B.; On log-Sobolev Inequalities for Infinite Lattice Systems, Lett. Math. Phys.20, 173-182 (1990) Zbl0717.47015MR1074698
  110. [110] Zegarlinski B.; Log-Sobolev Inequalities for Infinite One Dimensional Lattice Systems, Commun. Math. Phys.133, 147-162 (1990) Zbl0713.60080MR1071239
  111. [111] Zegarlinski B.; Dobrushin Uniqueness Theorem and Logarithmic Sobolev Inequalities, J. Funct. Anal.105, 77-111 (1992) Zbl0761.46020MR1156671
  112. [112] Zegarlinski B.; Hypercontractive Semigroups and Applications, Bochum Lecture Notes1992, unpublished 
  113. [113] Zegarlinski B.; Strong Decay to Equilibrium in One Dimensional Random Spin Systems. J. Stat. Phys.77, 717-732 (1994) Zbl0839.60102MR1301461
  114. [114] Zegarlinski B.; Ergodicity of Markov Semigroups. Proc. of the Conference : Stochastic Partial Differential Equations, Edinburgh1994, Ed. A. Etheridge, London Math Soc. Lect. Notes216, Cambridge University Press (1995) Zbl0824.47034MR1352750
  115. [115] Zegarlinski B.; The Strong Decay to Equilibrium for the Stochastic Dynamics of an Unbounded Spin System on a Lattice, Commun. Math. Phys.175, 401-432 (1996) Zbl0844.46050MR1370101
  116. [116] Zegarlinski B.; Isoperimetry for Gibbs measures, Ann. of Probab. (2001) Zbl1027.60099MR1849178
  117. [117] Zegarlinski B.; Entropy bounds for Gibbs Measures with non-Gaussian tails, J. Funct. Anal. to appear Zbl0992.60096MR1875152
  118. [118] Zegarlinski B.; Analysis of classical and quantum interacting particle systems, in Trento School 2000 Lecture Notes, World Scientific to appear MR1929790

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  4. Natalie Grunewald, Felix Otto, Cédric Villani, Maria G. Westdickenberg, A two-scale approach to logarithmic Sobolev inequalities and the hydrodynamic limit
  5. Alessandro Pizzo, David Renfrew, Alexander Soshnikov, On finite rank deformations of Wigner matrices

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