The maximum of log-correlated Gaussian fields in random environment

IF 3.1 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics Pub Date : 2023-11-02 DOI:10.1002/cpa.22181

Florian Schweiger, Ofer Zeitouni

{"title":"The maximum of log-correlated Gaussian fields in random environment","authors":"Florian Schweiger, Ofer Zeitouni","doi":"10.1002/cpa.22181","DOIUrl":null,"url":null,"abstract":"<p>We study the distribution of the maximum of a large class of Gaussian fields indexed by a box <math>\n <semantics>\n <mrow>\n <msub>\n <mi>V</mi>\n <mi>N</mi>\n </msub>\n <mo>⊂</mo>\n <msup>\n <mi>Z</mi>\n <mi>d</mi>\n </msup>\n </mrow>\n <annotation>$V_N\\subset \\mathbb {Z}^d$</annotation>\n </semantics></math> and possessing logarithmic correlations up to local defects that are sufficiently rare. Under appropriate assumptions that generalize those in Ding et al., we show that asymptotically, the centered maximum of the field has a randomly-shifted Gumbel distribution. We prove that the two dimensional Gaussian free field on a super-critical bond percolation cluster with <math>\n <semantics>\n <mi>p</mi>\n <annotation>$p$</annotation>\n </semantics></math> close enough to 1, as well as the Gaussian free field in i.i.d. bounded conductances, fall under the assumptions of our general theorem.</p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"77 5","pages":"2778-2859"},"PeriodicalIF":3.1000,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cpa.22181","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications on Pure and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/cpa.22181","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

Abstract

We study the distribution of the maximum of a large class of Gaussian fields indexed by a box $V_{N} \subset Z^{d}$ and possessing logarithmic correlations up to local defects that are sufficiently rare. Under appropriate assumptions that generalize those in Ding et al., we show that asymptotically, the centered maximum of the field has a randomly-shifted Gumbel distribution. We prove that the two dimensional Gaussian free field on a super-critical bond percolation cluster with $p$ close enough to 1, as well as the Gaussian free field in i.i.d. bounded conductances, fall under the assumptions of our general theorem.

Abstract Image

查看原文本刊更多论文

随机环境中对数相关高斯场的最大值

我们研究了一大类高斯场的最大值的分布，该类高斯场由一个盒VN⊂Zd$V_N\subet\mathbb｛Z｝^d$索引，并且具有对数相关性，直到足够罕见的局部缺陷。在适当的假设下，推广了Ding等人的假设。，我们证明了场的中心极大值渐近地具有随机移位的Gumbel分布。我们证明了p足够接近1的超临界键渗流簇上的二维高斯自由场，以及i.i.d.有界电导中的高斯自由场都属于我们的一般定理的假设。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Communications on Pure and Applied Mathematics 数学-数学

CiteScore

6.70

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.