Multivariate approximation in total variation, II: discrete normal approximation

TL;DR

This paper extends the theory of multivariate approximation in total variation to discrete normal approximation, demonstrating its application to sums of independent vectors, exchangeable pairs, and graph colorings.

Contribution

It introduces new methods for discrete normal approximation in total variation for multivariate cases, including sums, exchangeable pairs, and graph coloring applications.

Findings

Effective approximation of sums of independent integer vectors

Application to exchangeable pairs in multivariate settings

Demonstrated use in random graph colorings

Abstract

The paper applies the theory developed in Part I to the discrete normal approximation in total variation of random vectors in ${\mathbb Z}^d$. We illustrate the use of the method for sums of independent integer valued random vectors, and for random vectors exhibiting an exchangeable pair. We conclude with an application to random colourings of regular graphs.