11 papers
Darboux-type formula for Jacobi biorthogonal polynomials
Zhaofeng Lin, Kai Wang, Zhanhang Zheng
In this paper, we study the asymptotic behavior of Jacobi biorthogonal polynomials. A Darboux-type formula is established using the method of steepest descent. In the proof, we con…
Normal approximation for iterated inner functions
Yukun Chen, Xiangdi Fu, Zhaofeng Lin +1
A Berry--Esséen theorem for linear combinations of iterates of an inner function is obtained. Our proof, which is based an elementary transfer argument and classical results in mar…
Salem properties of Dvoretzky random coverings
Yukun Chen, Xiangdi Fu, Zhaofeng Lin +1
We establish the Salem properties for the uncovered sets in the celebrated Dvoretzky random coverings of the unit circle.
Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus
Yukun Chen, Zhaofeng Lin, Yanqi Qiu
We determine the exact values of the Fourier dimensions for Gaussian Multiplicative Chaos measures on the -dimensional torus for all integers . This reso…
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…
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…
Number rigid determinantal point processes induced by generalized Cantor sets
Zhaofeng Lin, Yanqi Qiu, Kai Wang
We consider the Ghosh-Peres number rigidity of translation-invariant determinantal point processes on the real line , whose correlation kernels are induced by the Fouri…
A Law of large numbers for vector-valued linear statistics of Bergman DPP
Zhaofeng Lin, Yanqi Qiu, Kai Wang
We establish a law of large numbers for a certain class of vector-valued linear statistics for the Bergman determinantal point process on the unit disk. Our result seems to be the…
Truncations of random unitary matrices drawn from Hua-Pickrell distribution
Zhaofeng Lin, Yanqi Qiu, Kai Wang
Let be a random unitary matrix drawn from the Hua-Pickrell distribution on the unitary group . We show that the eigenvalues of the…
Fluctuations of the process of moduli for the Ginibre and hyperbolic ensembles
Alexander I. Bufetov, David García-Zelada, Zhaofeng Lin
We investigate the point process of moduli of the Ginibre and hyperbolic ensembles. We show that far from the origin and at an appropriate scale, these processes exhibit Gaussian a…
Gaussian limit for determinantal point processes with -Hermitian kernels
Zhaofeng Lin, Yanqi Qiu, Kai Wang
We show that the central limit theorem for linear statistics over determinantal point processes with -Hermitian kernels holds under fairly general conditions. In particular, We…