3 papers
math.PR2025
The non-covered set in Dvoretzky covering is a set of multiplicity
Mingjie Tan
We prove that the non-covered set in Dvortezky random covering is a set of multiplicity, by showing that the natural multiplicative chaotic measure is a Rajchman measure.
math.PR2025
Harmonic analysis of multiplicative chaos Part II: a unified approach to Fourier dimensions
Zhaofeng Lin, Yanqi Qiu, Mingjie Tan
We introduce a unified approach for studying the polynomial Fourier decay of classical multiplicative chaos measures. As consequences, we obtain the precise Fourier dimensions for…
math.PR2025
Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC
Zhaofeng Lin, Yanqi Qiu, Mingjie Tan
In this paper, we establish the exact Fourier dimensions of all standard sub-critical Gaussian multiplicative chaos on the unit interval, thereby confirming the Garban-Vargas conje…