H\"older type estimates for Gaussian multiplicative chaos
Probability
2025-12-01 v1
Abstract
We investigate the right tail behavior of a certain class of GMC ratios, reminiscent of H\"older's inequality. We start with a heuristic argument to justify the optimal exponent in the tail estimate. Since Kahane's convexity inequality does not apply to GMC ratios, implementing the heuristic in the continuous setting is nontrivial from the viewpoint of GMC theory. We address the problem by enlarging the class of GMC ratios considered, and deduce the upper and lower bounds for the right tail of GMC ratios.
Keywords
Cite
@article{arxiv.2511.23033,
title = {H\"older type estimates for Gaussian multiplicative chaos},
author = {Yulai Huang},
journal= {arXiv preprint arXiv:2511.23033},
year = {2025}
}