A FLUCTUATION RESULT FOR THE DISPLACEMENT IN THE OPTIMAL MATCHING PROBLEM
成果类型：
Article
署名作者：
Goldman, Michael; Huesmann, Martin
署名单位：
Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); University of Munster
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/21-AOP1562
发表日期：
2022
页码：
1446-1477
关键词：
摘要：
The aim of this paper is to justify in dimensions two and three the ansatz of Caracciolo et al. stating that the displacement in the optimal matching problem is essentially given by the solution to the linearized equation that is, the Poisson equation. Moreover, we prove that at all mesoscopic scales, this displacement is close in suitable negative Sobolev spaces to a curl-free Gaussian free field. For this, we combine a quantitative estimate on the difference between the displacement and the linearized object, which is based on the large-scale regularity theory recently developed in collaboration with F. Otto, together with a qualitative convergence result for the linearized problem.