6 papers
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,…
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…
Canonical Mandelbrot Cascades on Curves Are Rajchman
Yin Cai, Guozheng Cheng, Xiang Fang +3
We settle the Rajchman problem for canonical scalar dyadic Mandelbrot cascades at the minimal Kahane--Peyrière integrability threshold. If is the cascade on , then $\wid…
Exact Fourier dimensions of dyadic Mandelbrot cascades on curves of nonvanishing curvature under minimal integrability
Yin Cai, Xiang Fang, Hongdou Qu
We prove exact Fourier-dimension formulas for scalar dyadic Mandelbrot cascades pushed forward to fixed nondegenerate embedded arcs and fixed nondegenerate Jordan curve…
Exact Fourier dimensions of dyadic Mandelbrot cascades under minimal integrability
Yin Cai, Guozheng Cheng, Xiang Fang +3
We determine the Fourier dimension of dyadic Mandelbrot cascades under the minimal Kahane-Peyriere integrability condition. The interval theorem is proved in a vector-valued dyadic…
Cut a Numeric String into Required Pieces
Yinqi Cai
We study the problem of cutting a length- string of positive real numbers into pieces so that every piece has sum at least . The problem can also be phrased as transformi…