In this work, we describe a method that determines an exact map from a finite set of
subgraph densities to the parameters of a stochastic block model (SBM) matching these …

We establish an invariance principle for polynomial functions of $ n $ independent high-
dimensional random vectors, and also show that the obtained rates are nearly optimal. Both …

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 …

Motivated by open problems in applied and computational algebraic topology, we establish
multivariate normal approximation theorems for three random vectors which arise …

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 …

The theory of graphons comes with a natural sampling procedure, which results in an
inhomogeneous variant of the Erdős–Rényi random graph, called W‐random graphs. We …

Real networks often exhibit clustering, the tendency to form relatively small groups of nodes
with high edge densities. This clustering property can cause large numbers of small and …

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 …

A key object of study in stochastic topology is a random simplicial complex. In this work we
study a multi-parameter random simplicial complex model, where the probability of including …

This paper studies the limiting behavior of the count of subgraphs isomorphic to a graph $ G
$ with $ m\geq 0$ fixed endpoints in the random-connection model, as the intensity …