## Multivariate approximation in total variation. II: Discrete normal approximation.(English)Zbl 1393.62008

Summary: The paper applies the theory developed in Part I [the authors, ibid. 46, No. 3, 1351–1404 (2018; Zbl 1393.62007)] 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.

### MSC:

 62E17 Approximations to statistical distributions (nonasymptotic) 62E20 Asymptotic distribution theory in statistics 60J27 Continuous-time Markov processes on discrete state spaces 60C05 Combinatorial probability 60F05 Central limit and other weak theorems

Zbl 1393.62007
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### References:

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