期刊
PROBABILITY THEORY AND RELATED FIELDS
卷 140, 期 1-2, 页码 19-40出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s00440-007-0056-3
关键词
granular media equation; transportation cost inequality; logarithmic Sobolev inequalities; concentration inequalities
We use here a particle system to prove both a convergence result (with convergence rate) and a deviation inequality for solutions of granular media equation when the confinement potential and the interaction potential are no more uniformly convex. The proof of convergence is simpler than the one in Carrillo-McCann-Villani (Rev. Mat. Iberoamericana 19:971-1018, 2003; Arch. Rat. Mech. Anal. 179:217-263, 2006). All the results complete former results of Malrieu (Ann. Appl. Probab. 13:540-560, 2003) in the uniformly convex case. The main tool is an uniform propagation of chaos property and a direct control in Wasserstein distance of solutions starting with different initial measures. The deviation inequality is obtained via a T (1) transportation cost inequality replacing the logarithmic Sobolev inequality which is no more clearly dimension free.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据