Harmonic analysis of Gaussian multiplicative chaos on the circle
Probability
2024-03-01 v2 Mathematical Physics
Functional Analysis
math.MP
Abstract
In this paper, we initiate the harmonic analysis of Gaussian multiplicative chaos (GMC) on the circle, i.e. the study of its Fourier coefficients. In particular, we show that almost surely GMC is a so-called Rajchman measure which means that its Fourier coefficients converge to when the frequency goes to infinity. We supplement this result with a convergence in law result for the rescaled Fourier coefficients.
Keywords
Cite
@article{arxiv.2311.04027,
title = {Harmonic analysis of Gaussian multiplicative chaos on the circle},
author = {Christophe Garban and Vincent Vargas},
journal= {arXiv preprint arXiv:2311.04027},
year = {2024}
}
Comments
23 pages