Thick points of high-dimensional Gaussian free fields

被引：2

作者：

Chen, Linan ^{[1
]}

机构：

[1] McGill Univ, Dept Math & Stat, 805 Sherbmoke St West, Montreal, PQ H3A 0B9, Canada

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2018年 / 54卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Gaussian free field; Polynomial singularity; Thick point; Hausdorff dimension; MULTIFRACTAL ANALYSIS; MULTIPLICATIVE CHAOS;

D O I：

10.1214/17-AIHP846

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：

This work aims to extend the existing results on thick points of logarithmic-correlated Gaussian Free Fields to Gaussian random fields that are more singular. To be specific, we adopt a sphere averaging regularization to study polynomial-correlated Gaussian Free Fields in higher-than-two dimensions. Under this setting, we introduce the definition of thick points which, heuristically speaking, are points where the value of the Gaussian Free Field is unusually large. We then establish a result on the Hausdorff dimension of the sets containing thick points.

引用

页码：1492 / 1526

页数：35

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