Universal tail profile of Gaussian multiplicative chaos

被引：0
作者：
Mo Dick Wong
机构：
[1] University of Oxford,Mathematical Institute
来源：
Probability Theory and Related Fields | 2020年 / 177卷
关键词：
Gaussian multiplicative chaos; Log-correlated Gaussian fields; Primary 60G57; Secondary 60G15; 28A80;
D O I：
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中图分类号：
学科分类号：
摘要：
In this article we study the tail probability of the mass of Gaussian multiplicative chaos. With the novel use of a Tauberian argument and Goldie’s implicit renewal theorem, we provide a unified approach to general log-correlated Gaussian fields in arbitrary dimension and derive precise first order asymptotics of the tail probability, resolving a conjecture of Rhodes and Vargas. The leading order is described by a universal constant that captures the generic property of Gaussian multiplicative chaos, and may be seen as the analogue of the Liouville unit volume reflection coefficients in higher dimensions.
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页码：711 / 746
页数：35
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