A geometric treatment of log-correlated Gaussian free fields

被引：10

作者：

Chen, Linan ^{[1
]}

Shu, Na ^{[1
]}

机构：

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

来源：

PROBABILISTIC METHODS IN GEOMETRY, TOPOLOGY AND SPECTRAL THEORY | 2019年 / 739卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Gaussian free field; Fourier-Bessel expansion; regularization; random measure; the KPZ formula; MULTIPLICATIVE CHAOS; THICK POINTS;

D O I：

10.1090/conm/739/14891

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

One way to regularize a log-correlated Gaussian free field (GFF) is to consider (functionals of) its spherical averages. In even dimensions, this regularization approach has been adopted in the construction of the Liouville Quantum Gravity (LQG) measure and the proof of the Knizhnik-Polyakov-Zamolodchikov (KPZ) formula (e.g. Chen and Jakobson, Ann. Henri Poincare 15 (2014), pp 1245-1283 and Duplantier, Rhodes, Sheffield, and Vargas, Invent. Math. 185 (2011) pp 333-393). In this article, we combine the Fourier-Bessel expansion with the spherical averages of the GFF to extend such a regularization approach to treat log-correlated GFFs in odd dimensions. We also outline the proofs of the existence of the LQG measure and the KPZ formula under this setting.

引用

页码：1 / 15

页数：15

共 22 条

[1] Gaussian Multiplicative Chaos and KPZ Duality [J].