The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off


  • Bakry, D.; Émery, Michel. Diffusions hypercontractives. (French) [Hypercontractive diffusions] Séminaire de probabilités, XIX, 1983/84, 177--206, Lecture Notes in Math., 1123, Springer, Berlin, 1985. MR0889476
  • Bertini, Lorenzo; Cancrini, Nicoletta; Cesi, Filippo. The spectral gap for a Glauber-type dynamics in a continuous gas. Ann. Inst. H. Poincaré Probab. Statist. 38 (2002), no. 1, 91--108. MR1899231
  • Boudou, Anne-Severine; Caputo, Pietro; Dai Pra, Paolo; Posta, Gustavo. Spectral gap estimates for interacting particle systems via a Bochner-type identity. J. Funct. Anal. 232 (2006), no. 1, 222--258. MR2200172
  • Caputo, Pietro; Dai Pra, Paolo; Posta, Gustavo. Convex entropy decay via the Bochner-Bakry-Emery approach. Ann. Inst. Henri Poincaré Probab. Stat. 45 (2009), no. 3, 734--753. MR2548501
  • Caputo, Pietro; Posta, Gustavo. Entropy dissipation estimates in a zero-range dynamics. Probab. Theory Related Fields 139 (2007), no. 1-2, 65--87. MR2322692
  • M. Disertori, A. Giuliani; phThe nematic phase of a system of long hard rods. Comm. Math. Phys. (to appear). ARXIV1112.5564v2.
  • Diaconis, P.; Saloff-Coste, L. Logarithmic Sobolev inequalities for finite Markov chains. Ann. Appl. Probab. 6 (1996), no. 3, 695--750. MR1410112
  • Erbar, Matthias; Maas, Jan. Ricci curvature of finite Markov chains via convexity of the entropy. Arch. Ration. Mech. Anal. 206 (2012), no. 3, 997--1038. MR2989449
  • Grunewald, Natalie; Otto, Felix; Villani, Cédric; Westdickenberg, Maria G. A two-scale approach to logarithmic Sobolev inequalities and the hydrodynamic limit. Ann. Inst. Henri Poincaré Probab. Stat. 45 (2009), no. 2, 302--351. MR2521405
  • Kelly, F. P. Loss networks. Ann. Appl. Probab. 1 (1991), no. 3, 319--378. MR1111523
  • Y. Kondratiev, K. Tobias, N. Ohlerich; phSpectral gap for Glauber type dynamics for a special class of potentials. ARXIV1103.5079v1
  • Ledoux, M. Logarithmic Sobolev inequalities for unbounded spin systems revisited. Séminaire de Probabilités, XXXV, 167--194, Lecture Notes in Math., 1755, Springer, Berlin, 2001. MR1837286
  • Levin, David A.; Peres, Yuval; Wilmer, Elizabeth L. Markov chains and mixing times. With a chapter by James G. Propp and David B. Wilson. American Mathematical Society, Providence, RI, 2009. xviii+371 pp. ISBN: 978-0-8218-4739-8 MR2466937
  • Li, Xiang-Dong. Perelman's entropy formula for the Witten Laplacian on Riemannian manifolds via Bakry-Emery Ricci curvature. Math. Ann. 353 (2012), no. 2, 403--437. MR2915542
  • Luby, Michael; Vigoda, Eric. Fast convergence of the Glauber dynamics for sampling independent sets. Statistical physics methods in discrete probability, combinatorics, and theoretical computer science (Princeton, NJ, 1997). Random Structures Algorithms 15 (1999), no. 3-4, 229--241. MR1716763
  • Ma, Yutao; Wang, Ran; Wu, Liming. Transportation-information inequalities for continuum Gibbs measures. Electron. Commun. Probab. 16 (2011), 600--613. MR2846653
  • Maas, Jan. Gradient flows of the entropy for finite Markov chains. J. Funct. Anal. 261 (2011), no. 8, 2250--2292. MR2824578
  • Vigoda, Eric. A note on the Glauber dynamics for sampling independent sets. Electron. J. Combin. 8 (2001), no. 1, Research Paper 8, 8 pp. (electronic). MR1814515
  • Wu, Liming. A new modified logarithmic Sobolev inequality for Poisson point processes and several applications. Probab. Theory Related Fields 118 (2000), no. 3, 427--438. MR1800540
  • Wu, Liming. Estimate of spectral gap for continuous gas. Ann. Inst. H. Poincaré Probab. Statist. 40 (2004), no. 4, 387--409. MR2070332

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.