arXiv subjects

Hui-Lin Liu

Publications and source records attributed to Hui-Lin Liu.

2 recordsLinked to original sources

arXiv2026

Refined Cramér-type moderate deviations by Stein's method under dependence

In this paper, we establish refined Cramér-type moderate deviations for dependent random variables at any fixed order $m\geq3$. Combining higher-order Stein identities with exponential tilting, we obtain cumulant-corrected tail approximations with explicit error bounds for boundedly supported kernels. Our main application gives a fourth-order expansion under bounded local dependence, reaching an $O(n^{3/10})$ deviation range under standard normalization with fixed dependence parameters. It improves on previous work in both deviation range and applicability, and also covers bounded $m$-dependent sequences without an independent-base representation. Further applications to the generalized combinatorial central limit theorem and the Curie-Weiss model also extend some earlier results under permutation and mean-field dependence.

math.PR↗

arXiv2026

Fluctuations of subgraph counts in exponential random graphs

In this paper, we study fluctuations of fixed subgraph counts in dense exponential random graphs on $n$ vertices. We compare each normalized subgraph count $V$ with the normalized edge count $W$: their difference $V-W$ is $O(n^{-1/2})$ in $L^2$, whereas $\mathbb{E}[(V-W)f(W)]=O(n^{-1})$ for every $1$-Lipschitz function $f$. We also obtain $O(n^{-1})$ Kolmogorov and Wasserstein bounds, optimal for the edge count, with relative variance error of the same order. These estimates hold uniformly on compact subsets of the ferromagnetic subcritical and absolute-coefficient Dobrushin regions, and under small fixed signed perturbations of the former. Using this uniform control, we derive a local Gaussian likelihood expansion with rank-one leading Fisher information and two-sided moderate deviations with an explicit cubic correction. The proofs combine two applications of the normal Stein equation, covariance estimates from Glauber dynamics and exponential tilting.

math.PR↗