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2018 Negative moments for Gaussian multiplicative chaos on fractal sets
Christophe Garban, Nina Holden, Avelio Sepúlveda, Xin Sun
Electron. Commun. Probab. 23: 1-10 (2018). DOI: 10.1214/18-ECP168

Abstract

The objective of this note is to study the probability that the total mass of a subcritical Gaussian multiplicative chaos (GMC) with arbitrary base measure $\sigma $ is small. When $\sigma $ has some continuous density w.r.t Lebesgue measure, a scaling argument shows that the logarithm of the total GMC mass is sub-Gaussian near $-\infty $. However, when $\sigma $ has no scaling properties, the situation is much less clear. In this paper, we prove that for any base measure $\sigma $, the total GMC mass has negative moments of all orders.

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Christophe Garban. Nina Holden. Avelio Sepúlveda. Xin Sun. "Negative moments for Gaussian multiplicative chaos on fractal sets." Electron. Commun. Probab. 23 1 - 10, 2018. https://doi.org/10.1214/18-ECP168

Information

Received: 28 May 2018; Accepted: 11 September 2018; Published: 2018
First available in Project Euclid: 19 December 2018

zbMATH: 07023489
MathSciNet: MR3896838
Digital Object Identifier: 10.1214/18-ECP168

Subjects:
Primary: 60D05, 60G15, 60G60

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