Multivariate approximation in total variation, II: discrete normal   approximation
  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. 
A. D. Barbour, Malwina J. Luczak, Aihua Xia
math.PR