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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
31/2010

LSI for Kawasaki dynamics with weak interaction

Georg Menz

Abstract

We consider a large lattice system of unbounded continuous spins that are governed by a Ginzburg-Landau type potential and a weak quadratic interaction. We derive the logarithmic Sobolev inequality (LSI) for Kawasaki dynamics uniform in the boundary data. The scaling of the LSI constant is optimal in the system size and our argument is independent of the geometric structure of the system. The proof consists of an application of the two-scale approach of Grunewald, Otto, Westdickenberg & Villani. Several ideas are needed to solve new technical difficulties due to the interaction. Let us mention the application of a new covariance estimate, a conditioning technique, and a generalization of the local Cramér theorem.

Received:
Jun 7, 2010
Published:
Jun 15, 2010
MSC Codes:
60K35, 60J25, 82B21
Keywords:
Logarithmic Sobolev inequality, Spin system, Kawasaki dynamics, Canonical ensemble, coarse-graining

Related publications

inJournal
2011 Repository Open Access
Georg Menz

LSI for Kawasaki dynamics with weak interaction

In: Communications in mathematical physics, 307 (2011) 3, pp. 817-860