On the Fourier Coefficients of critical Gaussian multiplicative chaos

2025/10/28 by Arguin, Louis-Pierre, Hamdan, Jad · 1 citation
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2510.24424

Abstract

We continue the study of the Fourier coefficients of Gaussian multiplicative chaos (GMC) recently initiated by Garban and Vargas. We show that the Fourier coefficients c_n of critical GMC on the unit interval converge to zero in probability as the frequency n tends to infinity, by establishing tightness for \(log n)|c_n|\_{n≥ 1}.

Citations

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Cited by

• Fourier dimension of imaginary Gaussian multiplicative chaos

Related

• Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC
• Critical Gaussian multiplicative chaos: a review
• Harmonic analysis of Gaussian multiplicative chaos on the circle
• Fourier dimension of imaginary Gaussian multiplicative chaos
• Critical Gaussian Multiplicative Chaos revisited