Song-Hao Liu

activity

20232026

collaborators

8 papers

math.PR2026

Sharp Cramér-type moderate deviation bounds for the self-normalized maximum of partial sums

Song-Hao Liu, Qi-Man Shao, Hao Shi +1

Let $X_{1}, X_{2}, \dots$ be i.i.d. random variables with zero mean and variance $σ^{2} \in (0, \infty)$ . In this paper, we establish a sharp Cramér-type moderate deviation for the self-norm…

math.PR2026

Mixing Time of Conditional Two Star Exponential Random Graphs

Xiao Fang, Song-Hao Liu, Xiaolin Wang

Two star exponential random graph models (ERGMs) are an interesting special case of both general ERGMs and mean-field Ising models. In this paper, we study two star ERGMs condition…

math.PR2026

The Central Limit Theorem and Berry--Esseen bound for logarithmic law of random determinants

Song-Hao Liu, Qi-Man Shao, Jing-Yu Xu

Let $A = (A_{n})_{n \geq 2}$ be a triangular array of random matrices, where $A_{n} = (a_{ij})_{1 \leq i, j \leq n}$ is an $n \times n$ random matrix with independent real entries satisfying $\math…

math.PR2026

Critical-Window Fluctuations and Disorder Universality for the Sherrington--Kirkpatrick Model

Yu Cheng, Song-Hao Liu, Qi-Man Shao +1

We establish free-energy fluctuation limits for the Ising Sherrington--Kirkpatrick model in the nonzero parts of its critical window. For fixed $b \neq = 0$ and $β_N=1+bN^{-1/3}\sqrt{\l…

math.PR2026

Cramér-type moderate deviation for double index permutation statistics

Songhao Liu, Qiman Shao, Jingyu Xu

We establish a Cramér-type moderate deviation theorem for double-index permutation statistics (DIPS). To the best of our knowledge, previous results only provided Berry-Esseen type…

math.PR2025

Conditional central limit theorems for exponential random graphs

Xiao Fang, Song-Hao Liu, Zhonggen Su +1

In this paper, we study the Exponential Random Graph Models (ERGMs) conditioning on the number of edges. In subcritical region of model parameters, we prove a conditional Central L…

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 $Σ$ and the strongly non-degenerate case. For t…