LSI for Kawasaki dynamics with weak interaction
The aim of the article is to establish a new logarithmic Sobolev inequality (LSI) with a view to understanding the long-time limit of a random dynamical system of (unbounded, continuous) spins on a lattice. The strategy is now quite well known: it consists in using an LSI for the probability measure of the spin system, which allows one to control a so-called entropy functional and to show convergence to equilibrium. But obtaining an LSI is a difficult step, and many improvements to the standard approach are needed here to treat the case of the Kawasaki spin dynamics. The article is well-written, with many details and explanations, but it is not completely self-contained (it is a summary of some portion of the author's PhD thesis).
scientific article; zbMATH DE number 5977582