Exponential decay of entropy in the random transposition and Bernoulli-Laplace models
Open Access
- 1 November 2003
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Applied Probability
- Vol. 13 (4), 1591-1600
- https://doi.org/10.1214/aoap/1069786512
Abstract
We give bounds on the exponential decay rate of entropy in the random transposition model and the Bernoulli--Laplace model which are independent of the number of sites and the number of particles. This is then used to give a bound on the time to stationarity in the total variation norm.This publication has 16 references indexed in Scilit:
- Entropy inequalities for unbounded spin systemsThe Annals of Probability, 2002
- On logarithmic Sobolev inequalities for continuous time random walks on graphsProbability Theory and Related Fields, 2000
- Concentration of measure and logarithmic Sobolev inequalitiesLecture Notes in Mathematics, 1999
- Logarithmic Sobolev inequality for some models of random walksThe Annals of Probability, 1998
- Logarithmic Sobolev inequality for generalized simple exclusion processesProbability Theory and Related Fields, 1997
- Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamicsCommunications in Mathematical Physics, 1993
- Comparison Theorems for Reversible Markov ChainsThe Annals of Applied Probability, 1993
- Diffusion of color in the simple exclusion processCommunications on Pure and Applied Mathematics, 1992
- Hydrodynamics and large deviation for simple exclusion processesCommunications on Pure and Applied Mathematics, 1989
- Time to Reach Stationarity in the Bernoulli–Laplace Diffusion ModelSIAM Journal on Mathematical Analysis, 1987