## The Annals of Probability

### Multivariate approximation in total variation, II: Discrete normal approximation

#### 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.

#### Article information

Source
Ann. Probab., Volume 46, Number 3 (2018), 1405-1440.

Dates
First available in Project Euclid: 12 April 2018

https://projecteuclid.org/euclid.aop/1523520020

Digital Object Identifier
doi:10.1214/17-AOP1205

Mathematical Reviews number (MathSciNet)
MR3785591

Zentralblatt MATH identifier
06894777

#### Citation

Barbour, A. D.; Luczak, M. J.; Xia, A. Multivariate approximation in total variation, II: Discrete normal approximation. Ann. Probab. 46 (2018), no. 3, 1405--1440. doi:10.1214/17-AOP1205. https://projecteuclid.org/euclid.aop/1523520020

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