3 papers
math.CA2026
A quantitative form of the planar Falconer distance theorem
Guozheng Cheng, Xiang Fang, Menghan Li +2
We give a quantitative planar form of a multiscale argument for Falconer's distance problem. For every , we obtain a positive lower bound for the Lebesgue measure of the dis…
math.PR2026
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…
math.PR2026
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…