Salem properties of Dvoretzky random coverings

2025/11/17 by Chen, Yukun, Fu, Xiangdi, Lin, Zhaofeng +1
#FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2511.13068

Abstract

We establish the Salem properties for the uncovered sets in the celebrated Dvoretzky random coverings of the unit circle.

Citations

• The non-covered set in Dvoretzky covering is a set of multiplicity
• Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus
• Harmonic analysis of multiplicative chaos Part II: a unified approach to Fourier dimensions
• Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC
• Fourier dimension of Mandelbrot multiplicative cascades
• Harmonic analysis of Mandelbrot cascades -- in the context of vector-valued martingales
• Harmonic analysis of Gaussian multiplicative chaos on the circle
• Spatially independent martingales, intersections, and applications

Related

• On μ-Dvoretzky random covering of the circle
• The non-covered set in Dvoretzky covering is a set of multiplicity
• Explicit Salem sets in ℝⁿ
• On genericity of non-uniform Dvoretzky coverings of the circle
• Certain results on uniform circle random covering problems