Thick points for a Gaussian Free Field in 4 dimensions

被引：4

作者：

Cipriani, Alessandra ^{[1
]}

Hazra, Rajat Subhra ^{[2
]}

机构：

[1] Weierstrass Inst Berlin, D-10117 Berlin, Germany

[2] Univ Zurich, Inst Math, CH-8057 Zurich, Switzerland

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2015年 / 125卷 / 06期

基金：

芬兰科学院; 瑞士国家科学基金会;

关键词：

KPZ; Liouville quantum gravity; Thick points; Hausdorff dimension; Abstract Wiener space; Bilaplacian; MULTIPLICATIVE CHAOS; ENTROPIC REPULSION; BROWNIAN-MOTION;

D O I：

10.1016/j.spa.2015.01.004

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 article is concerned with the study of fractal properties of thick points for a 4-dimensional Gaussian Free Field. We adopt the definition of Gaussian Free Field on R-4 introduced by Chen and Jakobson (2012) viewed as an abstract Wiener space with underlying Hilbert space H-2(R-4). We can prove that for 0 <= a <= 4, the Hausdorff dimension of the set of a-high points is 4 - a. We also show that the thick points give full mass to the Liouville Quantum Gravity measure on R-4. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：2383 / 2404

页数：22

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