Summary.
Let be a probability measure on the set {0,1, . . .,R} for some R∈ℕ and Λ L a cube of width L in ℤ d. Denote by μgc ΛL the (grand canonical) product measure on the configuration space on Λ L with as the marginal measure; here the superscript indicates the grand canonical ensemble. The canonical ensemble, denoted by μc ΛL,n , is defined by conditioning μgc ΛL given the total number of particles to be n. Consider the exclusion dynamics where each particle performs random walk with rates depending only on the number of particles at the same site. The rates are chosen such that, for every n and L fixed, the measure μc ΛL,n is reversible. We prove the logarithmic Sobolev inequality in the sense that ∫flogfdμc ΛL,n ≤ for any probability density f with respect to μc ΛL,n ; here the constant is independent of n or L and D denotes the Dirichlet form of the dynamics. The dependence on L is optimal.
Article PDF
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 22 May 1996 / In revised Form: 7 March 1997
Rights and permissions
About this article
Cite this article
Yau, HT. Logarithmic Sobolev inequality for generalized simple exclusion processes. Probab Theory Relat Fields 109, 507–538 (1997). https://doi.org/10.1007/s004400050140
Issue Date:
DOI: https://doi.org/10.1007/s004400050140