Search

MiS Preprint Repository

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
5/2011

Uniform logarithmic Sobolev inequalities for conservative spin systems with super-quadratic single-site potential.

Georg Menz and Felix Otto

Abstract

We consider a non-interacting unbounded spin system with conservation of the mean spin. We derive a uniform logarithmic Sobolev inequality (LSI) provided the single-site potential is a bounded perturbation of a strictly convex function. The scaling of the LSI constant is optimal in the system size. The argument adapts the two-scale approach of Grunewald, Otto, Westdickenberg, and Villani from the quadratic to the general case. Using an asymmetric Brascamp-Lieb type inequality for covariances we reduce the task of deriving a uniform LSI to the convexification of the coarse-grained Hamiltonian, which follows from a general local Cramèr theorem.

Received:
Feb 7, 2011
Published:
Feb 8, 2011
MSC Codes:
60K35, 60J25, 82B21
Keywords:
Logarithmic Sobolev inequality, Spin system, Kawasaki dynamics, Canonical ensemble, coarse-graining

Related publications

inJournal
2013 Repository Open Access
Georg Menz and Felix Otto

Uniform logarithmic Sobolev inequalities for conservative spin systems with super-quadratic single-site potential

In: The annals of probability, 41 (2013) 3B, pp. 2182-2224