Home | Contents | Submissions, editors, etc. | Login | Search | ECP
 Electronic Journal of Probability > Vol. 10 (2005) > Paper 15 open journal systems 


Logarithmic Sobolev Inequality for Zero--Range Dynamics: Independence of the Number of Particles

Paolo Dai Pra, Università di Padova, Italy
Gustavo Posta, Politecnico di Milano, Italy


Abstract
We prove that the logarithmic-Sobolev constant for Zero-Range Processes in a box of diameter L may depend on L but not on the number of particles. This is a first, but relevant and quite technical step, in the proof that this logarithmic-Sobolev constant grows as the square of L, that is presented in a forthcoming paper.


Full text: PDF

Pages: 525-576

Published on: June 13, 2005
Bibliography
  1. C. Ané, S. Blachère, D. Chafaï, P. Fougéres, I. Gentil, F. Malrieu, C. Roberto and G. Scheffer. Sur les inégalités de Sobolev logarithmiques. Panoramas et Synthéses, 10 (2000). Société Mathématique de France, Paris. Math. Review 2002g:46132
  2. N. Cancrini, F. Martinelli and C. Roberto. The logarithmic Sobolev constant of Kawasaki dynamics under a mixing condition revisited. Ann. Inst. H. Poincaré Probab. Statist. 38 (2002), no. 4, 385-436. Math. Review 2003j:82057
  3. P. Dai Pra and G. Posta. Logrithmic Sobolev Inequality for Zero-Range Dynamics, (2004) to appear on Ann. Probab. Math. Review number not available.
  4. C. Landim and C. Kipnis. Scaling limits of interacting particle systems. Grundlehren der Mathematischen Wissenschaften 320 (1999). Springer-Verlag, New York-Berlin. Math. Review 2000i:60001
  5. C. Landim, S. Sethuraman and S. R. S. Varadhan. Spectral gap for zero-range dynamics. Ann. Probab. 24 (1996), no. 4, 1871-1902. Math. Review 97j:60186
  6. Liggett T.M. Interacting particle systems. 276 (1985) Springer-Verlag, New York-Berlin. Math. Review 86e:60089
  7. S. T. Lu and H.-T. Yau. Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics. Comm. Math. Phys. 156 (1993), 399-433. Math. Review 95f:60122
  8. L. Miclo. An example of application of discrete Hardy's inequalities, Markov Process. Rel. Fields 5 (1999), no. 3, 319-330. Math. Review 2000h:60081
  9. G. Posta. Spectral Gap for an Unrestricted Kawasaki Type Dynamics, ESAIM Probability & Statistics 1 (1997), 145-181. Math. Review 98m:60157
















Research
Support Tool
Capture Cite
View Metadata
Printer Friendly
Context
Author Address
Action
Email Author
Email Others


Home | Contents | Submissions, editors, etc. | Login | Search | ECP

Electronic Journal of Probability. ISSN: 1083-6489