In 1946 Paul Halmos studied unbiased estimators of minimum variance, and planted the
seed from which the subject matter of the present monograph sprang. The author has …

The application of Stein's method of obtaining rates of convergence to the normal
distribution is illustrated in the context of random graph theory. Problems which exhibit a …

We consider the random variable S_ n, v (f)= ∑ i_1<...< i_v\leqq nf (X_ i_1,..., X_ i_v, Y_ i_1
i_2,..., Y_ i_ v-1 i_v), where X ii= 1/n and Y ij 1≦ i< i≦ n are two independent sequences of …

In this paper, we establish optimal Berry–Esseen bounds for the generalized U-statistics.
The proof is based on a new Berry–Esseen theorem for exchangeable pair approach by …

Given a graphon and a finite simple graph, with vertex set, denote by the number of copies
of in a-random graph on vertices. The asymptotic distribution of was recently obtained by …

We give asymptotics for the cumulative distribution function (CDF) for degrees of large
dense random graphs sampled from a graphon. The proof is based on precise asymptotics …

As widely regarded, one of the most classical and remarkable tools to measure the
asymptotic normality of combinatorial statistics is due to Harper's real-rooted method …

Exchangeable random graphs, which include some of the most widely studied network
models, have emerged as the mainstay of statistical network analysis in recent years …

In this paper we consider a dynamic Erd\H {o} sR\'{e} nyi random graph with independent
identically distributed edge processes. Our aim is to describe the joint evolution of the …

Extending a previous result of the first two authors, we prove a local limit theorem for the joint
distribution of subgraph counts in the Erd\H {o} sR\'{e} nyi random graph $ G (n, p) $. This …