Author

W. Verreault

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Preprint Sep 2026

Fourier decay of Gaussian multiplicative chaos and boundary geometry

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 bo...

Marcu-Antone Orsoni, W. Verreault · 1 citation

Preprint Aug 2026

Almost sure upper bound for sums of random multiplicative functions and critical chaos

Let $f$ be a Steinhaus or Rademacher random multiplicative function. We use methods from the theory of critical chaos to improve on the best known upper bound for partial sums of random multiplicative functions. In particular, our results imply that for any $\varepsilon>0$, almost surely $$ \Big|\sum_{n\le x}f(n)\Big|...

W. Verreault · 1 citation · ⚡1