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math.PR2026
Fourier asymptotics of critical Gaussian multiplicative chaos on the circle
Yin Cai, Bonan Chen, Xiang Fang +1
We study the high-frequency Fourier coefficients of critical Gaussian multiplicative chaos on the circle, for logarithmic covariances with an arbitrary admissible smooth,…
math.PR2026
Critical Gaussian Multiplicative Chaos on the Circle Is Rajchman
Yin Cai, Bonan Chen, Xiang Fang +1
We prove that the Fourier coefficients of the canonical critical Gaussian multiplicative chaos on the circle vanish almost surely at infinity. More precisely, let $M_ϕ^{\mathrm{cri…
math.PR2026
Hardy-Szegő Point Processes: Large Deviations and Strong Szegő Asymptotics
Qian Ai, Xiang Fang, Shengzhao Hou
We study exponential-scale fluctuations of the Hardy-Szegő zero process, investigated by Peres and Virág in the disk setting, in its upper-half-plane realization, which reveals a d…