Open Access
Translator Disclaimer
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


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.


Download Citation

Christophe Garban. Nina Holden. Avelio Sepúlveda. Xin Sun. "Negative moments for Gaussian multiplicative chaos on fractal sets." Electron. Commun. Probab. 23 1 - 10, 2018.


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

Primary: 60D05 , 60G15 , 60G60

Keywords: Gaussian free field , Liouville measure , log-correlated fields , negative moments


Back to Top