LSI for Kawasaki dynamics with weak interaction
type: Item
instance of: scholarly article
title: LSI for Kawasaki dynamics with weak interaction
zbMATH Open document ID: 1266.82038
author: Georg Menz
published in: Communications in Mathematical Physics
publication date: 2011-11-23T00:00:00Z
review text: 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).
reviewed by: Sebastien Boyabal
Mathematics Subject Classification ID: 82C20
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 5977582
zbMATH Keywords: Kawasaki dynamics
zbMATH Keywords: spin lattice
zbMATH Keywords: logarithmic Sobolev inequality
MaRDI profile type: Publication
full work available at URL: s00220-011-1326-6
OpenAlex ID: W2063650345
cites work: The log-Sobolev inequality for unbounded spin systems
cites work: Q4545075
cites work: The logarithmic Sobolev constant of Kawasaki dynamics under a mixing condition revisited
cites work: Uniform Poincaré inequalities for unbounded conservative spin systems: the non-interacting case.
cites work: Q4453890
cites work: Q5624436
cites work: Logarithmic Sobolev Inequalities
cites work: A two-scale approach to logarithmic Sobolev inequalities and the hydrodynamic limit
cites work: Séminaire de Probabilités XXXVI
cites work: Nonlinear diffusion limit for a system with nearest neighbor interactions
cites work: Remarks on decay of correlations and Witten Laplacians. III: Application to logarithmic Sobolev inequalities
cites work: Logarithmic Sobolev inequalities and stochastic Ising models
cites work: Q4223675
cites work: The behavior of the specific entropy in the hydrodynamic scaling limit
cites work: Spectral gap and logarithmic Sobolev inequality for unbounded conservative spin systems
cites work: Q2725606
cites work: Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics
cites work: Uniform logarithmic Sobolev inequalities for conservative spin systems with super-quadratic single-site potential
cites work: A new criterion for the logarithmic Sobolev inequality and two applications
cites work: Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
cites work: Q4256258
cites work: Q4223074
cites work: The equivalence of the logarithmic Sobolev inequality and the Dobrushin- Shlosman mixing condition
cites work: The logarithmic Sobolev inequality for discrete spin systems on a lattice
cites work: On the ergodic properties of Glauber dynamics.
cites work: Relative entropy and hydrodynamics of Ginzburg-Landau models
cites work: Logarithmic Sobolev inequality for lattice gases mixing conditions
cites work: Application of log-Sobolev inequality to the stochastic dynamics of unbounded spin systems on the lattice
cites work: The equivalence of the log-Sobolev inequality and a mixing condition for unbounded spin systems on the lattice
cites work: The strong decay to equilibrium for the stochastic dynamics of unbounded spin systems on a lattice
DOI: 10.1007/S00220-011-1326-6
description: scientific article; zbMATH DE number 5977582