文章基本信息

标题：Negative moments for Gaussian multiplicative chaos on fractal sets
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作者：Christophe Garban ; Nina Holden ; Avelio Sepúlveda 等
期刊名称：Electronic Communications in Probability
印刷版ISSN：1083-589X
出版年度：2018
卷号：23
DOI：10.1214/18-ECP168
语种：English
出版社：Electronic Communications in Probability
摘要：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.