THE TRANSPORTATION COST FROM THE UNIFORM MEASURE TO THE EMPIRICAL MEASURE IN DIMENSION GREATER-THAN-OR-EQUAL-TO-3

• 成果类型: Article
• 署名作者: TALAGRAND, M
• 署名单位: University System of Ohio; Ohio State University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176988735
• 发表日期: 1994
• 页码: 919-959
• 关键词: Minimax

摘要

Consider two independent sequences (X(i))i less-than-or-equal-to n and (X(i)')i less-than-or-equal-to n that are independent and uniformly distributed over [0, 1]d, d greater-than-or-equal-to 3. Under mild regularity conditions, we describe the convex functions phi such that, with large probability, there exists a one-to-one map pi from {1, ..., n} to {1, ..., n} for which [GRAPHICS] where K(p) depends on phi only