WASSERSTEIN CONVERGENCE RATES OF INCREASINGLY CONCENTRATING PROBABILITY MEASURES
成果类型：
Article
署名作者：
Hasenpflug, Mareike; Rudolf, Daniel; Sprungk, Bjoern
署名单位：
University of Passau; Technical University Freiberg
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/23-AAP2040
发表日期：
2024
页码：
3320-3347
关键词：
摘要：
For l : R-d -> [0,infinity) we consider the sequence of probability measures (mu(n))(n is an element of N), where mu(n) is determined by a density that is proportional to exp(-nl). We allow for infinitely many global minimal points of l, as long as they form a finite union of compact manifolds. In this scenario, we show estimates for the p-Wasserstein convergence of (mu(n))(n is an element of N) to its limit measure. Imposing regularity conditions we obtain a speed of convergence of n(-1/(2p)) and adding a further technical assumption, we can improve this to a p-independent rate of 1/2 for all orders p is an element of N of the Wasserstein distance.