STEIN KERNELS AND MOMENT MAPS

• 成果类型: Article
• 署名作者: Fathi, Max
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/18-AOP1305
• 发表日期: 2019
• 页码: 2172-2185
• 关键词: brunn-minkowski; inequalities; transportation

摘要

We describe a construction of Stein kernels using moment maps, which are solutions to a variant of the Monge-Ampere equation. As a consequence, we show how regularity bounds in certain weighted Sobolev spaces on these maps control the rate of convergence in the classical central limit theorem, and derive new rates in Kantorovitch-Wasserstein distance in the log-concave situation, with explicit polynomial dependence on the dimension.