The non-covered set in Dvoretzky covering is a set of multiplicity
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.PR↗
arXiv subjects
Mingjie Tan
Publications and source records attributed to Mingjie Tan.
Harmonic analysis of multiplicative chaos Part II: a unified approach to Fourier dimensions
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 multiplicative chaos measures arising from the following key models: the sub-critical 1D and 2D GMC (which in particular resolves the Garban-Vargas conjecture); the sub-critical $d$-dimensional GMC with $d \ge 3$ when the parameter $\gamma$ is near the critical value; the canonical Mandelbrot random coverings; the canonical Mandelbrot cascades. For various other models, we establish the non-trivial lower bounds of the Fourier dimensions and in various cases we conjecture that they are all optimal and provide the exact values of Fourier dimensions.
math.PR↗
Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC
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 conjecture. The proof relies on a significant improvement of the vector-valued martingale method, initially developed by Chen-Han-Qiu-Wang in the studies of the Fourier dimensions of Mandelbrot cascade random measures.
math.PR↗