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May 2013 Uniform logarithmic Sobolev inequalities for conservative spin systems with super-quadratic single-site potential
Georg Menz, Felix Otto
Ann. Probab. 41(3B): 2182-2224 (May 2013). DOI: 10.1214/11-AOP715

Abstract

We consider a noninteracting 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, Villani, Westdickenberg and the second author 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 Cramér theorem.

Citation

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Georg Menz. Felix Otto. "Uniform logarithmic Sobolev inequalities for conservative spin systems with super-quadratic single-site potential." Ann. Probab. 41 (3B) 2182 - 2224, May 2013. https://doi.org/10.1214/11-AOP715

Information

Published: May 2013
First available in Project Euclid: 15 May 2013

zbMATH: 1282.60096
MathSciNet: MR3098070
Digital Object Identifier: 10.1214/11-AOP715

Subjects:
Primary: 60K35
Secondary: 60J25, 82B21

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 3B • May 2013
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