A PDE approach to a 2-dimensional matching problem

• 成果类型: Article
• 署名作者: Ambrosio, Luigi; Stra, Federico; Trevisan, Dario
• 署名单位: Scuola Normale Superiore di Pisa; University of Pisa
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-018-0837-x
• 发表日期: 2019
• 页码: 433-477
• 关键词: curvature-dimension condition; transportation cost; CONVERGENCE

摘要

We prove asymptotic results for 2-dimensional random matching problems. In particular, we obtain the leading term in the asymptotic expansion of the expected quadratic transportation cost for empirical measures of two samples of independent uniform random variables in the square. Our technique is based on a rigorous formulation of the challenging PDE ansatz by Caracciolo et al. (Phys Rev E 90:012118, 2014) that linearizes the Monge-Ampere equation.