3 papers
math.PR2025
Central limit theorem for high temperature spin models via martingale embedding
Xiao Fang, Yang Xie, Yi-Kun Zhao
We use martingale embeddings to prove a central limit theorem (CLT) for one-dimensional projections of high-dimensional random vectors in satisfying a Poincaré inequal…
math.PR2024
Normal approximation for exponential random graphs
Xiao Fang, Song-Hao Liu, Qi-Man Shao +1
The question of whether the central limit theorem (CLT) holds for the total number of edges in exponential random graph models (ERGMs) in the subcritical region of parameters has r…
math.PR2023
High-dimensional Central Limit Theorems by Stein's Method in the Degenerate Case
Xiao Fang, Yuta Koike, Song-Hao Liu +1
In the literature of high-dimensional central limit theorems, there is a gap between results for general limiting correlation matrix and the strongly non-degenerate case. For t…