An Inductive Proof of the Berry-Esseen Theorem for Character Ratios

Higher Dimensional Quasi-Power Theorem and Berry-Esseen Inequality

Hwang's quasi-power theorem asserts that a sequence of random variables whose moment generating functions are approximately given by powers of some analytic function is asymptotically normally distributed. This theorem is generalised to higher dimensional random variables. To obtain this result, a higher dimensional analogue of the Berry-Esseen inequality is proved, generalising a two-dimensional version by Sadikova.

Discrete Malliavin-Stein method: Berry-Esseen bounds for random graphs and percolation

A new Berry-Esseen bound for non-linear functionals of non-symmetric and non-homogeneous infinite Rademacher sequences is established. It is based on a discrete version of the Malliavin-Stein method and an analysis of the discrete Ornstein-Uhlenbeck semigroup. The result is applied to sub-graph counts and to the number of vertices having a prescribed degree in the Erdős-Renyi random graph. A further application deals with a percolation problem on trees.

On the Higher Dimensional Quasi-Power Theorem and a Berry-Esseen Inequality

Hwang's quasi-power theorem asserts that a sequence of random variables whose moment generating functions are approximately given by powers of some analytic function is asymptotically normally distributed. This theorem is generalised to higher dimensional random variables. To obtain this result, a higher dimensional analogue of the Berry-Esseen inequality is proved, generalising a two-dimensional version of Sadikova.

随机张量的反集中与Berry--Esseen界

Anticoncentration and Berry--Esseen bounds for random tensors

本文研究了随机张量线性函数的反集中与Berry-Esseen界，提出高维张量组合CLT作为关键技术，并在任意维度推广了Bolthausen及Barbour/Chen的经典结果。

不完全等重复设计的U统计量：Berry-Esseen界与高效构造

Incomplete U-Statistics of Equireplicate Designs: Berry-Esseen Bound and Efficient Construction

本文提出基于超图理论和组合设计的U统计量新方法，推导Berry-Esseen界并高效构造不完全U统计量，解决退化情况下的高斯极限分布问题。

随机正则图的定量边缘特征向量普适性：带显式常数的Berry-Esseen界

Quantitative Edge Eigenvector Universality for Random Regular Graphs: Berry-Esseen Bounds with Explicit Constants

本文首次为随机正则图的边缘特征向量统计量建立了带显式常数的定量Berry-Esseen界，通过受约束Dyson Brownian运动的单尺度比较方法和尖锐边缘各向同性局部律，证明了N^{−1/6}的最优收敛速率，并推广到前K个边缘特征向量的联合普适性。