Multivariate Poisson approximation of joint subgraph counts in random graphs via size-biased couplings

TL;DR

This paper develops a multivariate Poisson approximation method for joint subgraph counts in random graphs using Chen-Stein and size-biased couplings, providing explicit convergence rates.

Contribution

It introduces a novel approach combining Chen-Stein and size-biased couplings for multivariate Poisson approximation with explicit error bounds.

Findings

Effective approximation of joint subgraph counts in Erdős-Rényi graphs

Explicit convergence rates for multivariate hypergeometric distribution

Enhanced understanding of subgraph count distributions in random graphs

Abstract

Using Chen-Stein method in combination with size-biased couplings, we obtain the multivariate Poisson approximation in terms of the Wasserstein distance. As applications, we study the multivariate Poisson approximation of the distribution of joint subgraph counts in an Erd\H{o}s-R\'enyi random graph and the multivariate hypergeometric distribution giving explicit convergence rates.