@article{d0ed03fbf6ee43c689e8ae12fbd55db9,

title = "Negative moments for gaussian multiplicative chaos on fractal sets",

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 σ is small. When σ 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 −∞. However, when σ has no scaling properties, the situation is much less clear. In this paper, we prove that for any base measure σ, the total GMC mass has negative moments of all orders.",

keywords = "Gaussian free field, Liouville measure, Log-correlated fields, Negative moments",

author = "Christophe Garban and Nina Holden and Avelio Sep{\'u}lveda and Xin Sun",

note = "Funding Information: Acknowledgments. The research of C.G. is supported by the ANR grant Liouville ANR-15-CE40-0013 and the ERC grant LiKo 676999. The research of N.H. is partially supported by a fellowship from the Norwegian Research Council. The research of A.S. is supported by the ERC grant LiKo 676999. The research of X.S. is supported by Simons Society of Fellows under Award 527901. The work on this paper started during the visit of N.H. and X.S. to Lyon in November 2017. They thank for the hospitality and for the funding through the ERC grant LiKo 676999. Publisher Copyright: {\textcopyright} 2018, Institute of Mathematical Statistics. All rights reserved.",

year = "2018",

doi = "10.1214/18-ECP168",

language = "English (US)",

volume = "23",

pages = "1--10",

journal = "Electronic Communications in Probability",

issn = "1083-589X",

publisher = "Institute of Mathematical Statistics",

}