EXTREME VALUES FOR TWO-DIMENSIONAL DISCRETE GAUSSIAN FREE FIELD

被引：28

作者：

Ding, Jian

Zeitouni, Ofer

机构：

[1] Stanford Univ, Stanford, CA 94305 USA

[2] MSRI, Berkeley, CA USA

[3] Univ Minnesota, Minneapolis, MN 55455 USA

[4] Weizmann Inst Sci, Dept Math, IL-76100 Rehovot, Israel

来源：

ANNALS OF PROBABILITY | 2014年 / 42卷 / 04期

基金：

以色列科学基金会; 美国国家科学基金会;

关键词：

Discrete Gaussian free fields; extreme values; right tails; COVER TIMES; BROWNIAN-MOTION; EQUATION; MAXIMUM; GRAPHS;

D O I：

10.1214/13-AOP859

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：1480 / 1515

页数：36

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