EXTREME VALUES FOR TWO-DIMENSIONAL DISCRETE GAUSSIAN FREE FIELD

• 成果类型: Article
• 署名作者: Ding, Jian; Zeitouni, Ofer
• 署名单位: Stanford University; University of Minnesota System; University of Minnesota Twin Cities; Weizmann Institute of Science
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/13-AOP859
• 发表日期: 2014
• 页码: 1480-1515
• 关键词: cover times; brownian-motion; equation; maximum; graphs

摘要

We consider in this paper the collection of near maxima of the discrete, two dimensional Gaussian free field in a box with Dirichlet boundary conditions. We provide a rough description of the geometry of the set of near maxima, estimates on the gap between the two largest maxima, and an estimate for the right tail up to a multiplicative constant on the law of the centered maximum.