40 citations · 54 across the 13 of their papers we have counts for
13 papers
An Analogue of Bernstein-Zelevinsky Derivatives to Automorphic Forms
Zhuohui Zhang
In this paper, a construction to imitate the Bernstein-Zelevinsky derivative for automorphic representations on is introduced. We will later consider the induced…
Some Combinatorics in the Cancellation of Poles of Eisenstein Series for
Zhuohui Zhang
The cancellations of poles of degenerate Eisenstein series were studied by Hanzer and Muić. This paper generalizes the method and the result to Eisenstein series constructed from i…
Cramér-type Moderate deviations under local dependence
Song-Hao Liu, Zhuo-Song Zhang
We establish Cramér-type moderate deviation theorems for sums of locally dependent random variables and combinatorial central limit theorems. Under some mild exponential moment con…
Dense multigraphon-valued stochastic processes and edge-changing dynamics in the configuration model
Adrian Röllin, Zhuo-Song Zhang
Time-evolving random graph models have appeared and have been studied in various fields of research over the past decades. However, the rigorous mathematical treatment of large gra…
Berry--Esseen bounds for self-normalized sums of local dependent random variables
Zhuo-Song Zhang
In this paper, we prove a Berry--Esseen bound with optimal order for self-normalized sums of local dependent random variables under some mild dependence conditions. The proof is ba…
Berry--Esseen bounds for generalized statistics
Zhuo-Song Zhang
In this paper, we establish optimal Berry--Esseen bounds for the generalized -statistics. The proof is based on a new Berry--Esseen theorem for exchangeable pair approach by Ste…
Berry--Esseen Bounds for Multivariate Nonlinear Statistics with Applications to M-estimators and Stochastic Gradient Descent Algorithms
Qi-Man Shao, Zhuo-Song Zhang
We establish a Berry--Esseen bound for general multivariate nonlinear statistics by developing a new multivariate-type randomized concentration inequality. The bound is the best po…
Littlewood-Richardson Coefficient, Springer Fibers and the Annihilator Varieties of Induced Representations
Zhuohui Zhang
For and a parabolic subgroup with a two-block Levi subgroup , the space , where $\…
Intertwining Operator for and Orthogonal Polynomials
Zhuohui Zhang
We calculate the module structure for the principal series representation of . Furthermore, we introduced a hypergeometric generating function…
Principal Series Representation of and Its Intertwining Operator
Zhuohui Zhang
In this paper, following a similar procedure developed by Buttcane and Miller in \cite{MillerButtcane} for $SL(3,\RR)$, the $(\frakg,K)$-module structure of the minimal principal s…
Cramér-type moderate deviation of normal approximation for unbounded exchangeable pairs
Zhuo-Song Zhang
In Stein's method, the exchangeable pair approach is commonly used to estimate the approximation errors in normal approximation. In this paper, we establish a Cramér-type moderate…
Cramér-type Moderate Deviation Theorems for Nonnormal Approximation
Qi-Man Shao, Mengchen Zhang, Zhuo-Song Zhang
A Cramér-type moderate deviation theorem quantifies the relative error of the tail probability approximation. It provides theoretical justification when the limiting tail probabili…
Berry-Esseen Bounds of Normal and Non-normal Approximation for Unbounded Exchangeable Pairs
Qi-Man Shao, Zhuo-Song Zhang
An exchangeable pair approach is commonly taken in the normal and non-normal approximation using Stein's method. It has been successfully used to identify the limiting distribution…