6 papers
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…
Strict correlation-dimension drop for quartic Salem Bernoulli convolutions
Guozheng Cheng, Xiang Fang, Xueqing Ma +1
For every quartic Salem number , we prove that the Bernoulli convolution with equal weights has correlation dimension strictly less than one. In particular,…
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…
Fourier Dimensions of Mandelbrot Cascades under Minimal Integrability
Xiang Fang
This note announces exact Fourier dimension formulas for canonical Mandelbrot cascade measures under the minimal Kahane Peyriere integrability condition and records the canonical b…
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…