UNIFORM LOGARITHMIC SOBOLEV INEQUALITIES FOR CONSERVATIVE SPIN SYSTEMS WITH SUPER-QUADRATIC SINGLE-SITE POTENTIAL

• 成果类型: Article
• 署名作者: Menz, Georg; Otto, Felix
• 署名单位: Max Planck Society
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP715
• 发表日期: 2013
• 页码: 2182-2224
• 关键词: spectral gap; kawasaki; DYNAMICS; limit

摘要

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 Cramer theorem.