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arXiv · 2510.24424

On the Fourier coefficients of critical Gaussian multiplicative chaos

Louis-Pierre Arguin·Jad Hamdan
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Abstract

We continue the study of the Fourier coefficients of Gaussian multiplicative chaos (GMC) recently initiated by Garban and Vargas. We show that if $\{c_n\}_{n\geq 1}$ are the Fourier coefficients of critical GMC on the unit interval, then $(\log n)^{\alpha}c_n$ converges to zero in probability as $n$ tends to infinity for any $\alpha<1/4$.

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Louis-Pierre Arguin, Jad Hamdan. 2025-10-28. On the Fourier coefficients of critical Gaussian multiplicative chaos. https://arxiv.org/abs/2510.24424

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