We prove that for the normalized sum $W=\sum_{i=1}^n X_i/\sqrt{n}$ of independent, mean-zero, $d$-dimensional random vectors with $\operatorname{Cov}(W) =\Sigma=\operatorname{diag}(\sigma_1^2,\dots, \sigma_d^2)$ (the diagonal form of the covariance matrix is assumed without loss of generality), the 2-Wasserstein distan...
Xiao Fang, Zi-Yao Su, Jiao-Xue Wang et al.· 0 citations
Let $X_N(t)$, $t\in[0,\pi]$, be a stationary Gaussian trigonometric polynomial, and let $\mathcal Z_N$ denote the number of zeros of the rescaled process $X_N(t/N)$ on $[0,N\pi]$. We establish the quantitative central limit theorem \[ d_{\mathrm W}\left( \frac{\mathcal Z_N-\mathbb E[\mathcal Z_N]} {\sqrt{\operatorname{...
Ao Huang, Zhong-Gen Su, Xiao-Lin Wang· 0 citations
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 conditioning on the edge density $p$. We begin with an analytic characterization of the replica symmetric region, where the conditional model is clos...
