6 papers
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…
The Central Limit Theorem and Berry--Esseen bound for logarithmic law of random determinants
Song-Hao Liu, Qi-Man Shao, Jing-Yu Xu
Let be a triangular array of random matrices, where is an random matrix with independent real entries satisfying $\math…
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 and $β_N=1+bN^{-1/3}\sqrt{\l…
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…
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…
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…