PreprintCC BY 4.0arXiv
Fourier decay of Gaussian multiplicative chaos and boundary geometry
Abstract
In this paper, we develop a new approach to studying the Fourier transform of Gaussian multiplicative chaos. We determine the Fourier dimension of these random measures on tori for every smooth log-correlated covariance and in every dimension, and prove sharp bounds and exact formulas for chaos on natural classes of bounded sets and hypersurfaces in Euclidean space. These results highlight how boundary geometry and multifractal concentration jointly govern Fourier decay, including regimes in which the boundary strictly reduces the Fourier dimension. In the circle setting, this gives a substantially simpler new proof of a conjecture of Garban and Vargas.
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BibTeX
@misc{orsoni2026fourier,
title = {{Fourier decay of Gaussian multiplicative chaos and boundary geometry}},
author = {Marcu-Antone Orsoni and William Verreault},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11761},
eprint = {2609.11761},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11761},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fourier decay of Gaussian multiplicative chaos and boundary geometry
AU - Marcu-Antone Orsoni
AU - William Verreault
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11761
UR - https://arxiv.org/abs/2609.11761
AB - In this paper, we develop a new approach to studying the Fourier transform of Gaussian multiplicative chaos. We determine the Fourier dimension of these random measures on tori for every smooth log-correlated covariance and in every dimension, and prove sharp bounds and exact formulas for chaos on natural classes of bounded sets and hypersurfaces in Euclidean space. These results highlight how boundary geometry and multifractal concentration jointly govern Fourier decay, including regimes in which the boundary strictly reduces the Fourier dimension. In the circle setting, this gives a substantially simpler new proof of a conjecture of Garban and Vargas.
ER -