DIMENSIONAL IMPROVEMENTS OF THE LOGARITHMIC SOBOLEV, TALAGRAND AND BRASCAMP-LIEB INEQUALITIES
DIMENSIONAL IMPROVEMENTS OF THE LOGARITHMIC SOBOLEV, TALAGRAND AND BRASCAMP-LIEB INEQUALITIES
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DOI：
10.1214/17-aop1184
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发表时间：
2018-01-01
影响因子：
2.3
通讯作者：
Guillin, Arnaud
中科院分区：
文献类型：
--
作者：
Bolley, Francois;Gentil, Ivan;Guillin, Arnaud
在这项工作中，我们考虑对数 Sobolev、Talagrand 和 Brascamp-Lieb 不等式的维度改进。为此，我们使用最优传输方法和 Borell-Brascamp-Lieb 不等式。这些改进可以写成经典不等式的缺陷。它们在尺寸方面具有正确的比例。它们导致随机微分方程解定律的锐化浓度特性以及精细收缩界限、收敛到平衡和短时行为。
In this work, we consider dimensional improvements of the logarithmic Sobolev, Talagrand and Brascamp-Lieb inequalities. For this, we use optimal transport methods and the Borell-Brascamp-Lieb inequality. These refinements can be written as a deficit in the classical inequalities. They have the right scale with respect to the dimension. They lead to sharpened concentration properties as well as refined contraction bounds, convergence to equilibrium and short time behavior for the laws of solutions to stochastic differential equations.