LAZY RANDOM WALKS AND OPTIMAL TRANSPORT ON GRAPHS

• 成果类型: Article
• 署名作者: Leonard, Christian
• 署名单位: Universite Paris Saclay
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/15-AOP1012
• 发表日期: 2016
• 页码: 1864-1915
• 关键词: metric-measure-spaces; RICCI CURVATURE; entropy; INEQUALITY; convexity; EXISTENCE; geometry; MAPS

摘要

This paper is about the construction of displacement interpolations of probability distributions on a discrete metric graph. Our approach is based on the approximation of any optimal transport problem whose cost function is a distance on a discrete graph by a sequence of entropy minimization problems under marginal constraints, called Schrodinger problems, which are associated with random walks. Displacement interpolations are defined as the limit of the time-marginal flows of the solutions to the Schrodinger problems as the jump frequencies of the random walks tend down to zero. The main convergence results are based on Gamma-convergence of entropy minimization problems. As a by-product, we obtain new results about optimal transport on graphs.