Inverse of the Gaussian multiplicative chaos: Moments

Ilia Binder, Tomas Kojar

Published 2023-04-30Version 1

In this article, we study the general properties and moments of the inverse of the Gaussian mutliplicative chaos. It is the first part of the preliminary work needed for extending the work in "Random conformal weldings" (by K. Astala, P. Jones, A. Kupiainen, E. Saksman) to the existence of Lehto welding for the inverse. In particular, we prove that the dilation of the inverse homeomorphism on the positive real line is in $L^{1}([0,1]\times[0,2])$.