On the Poisson approximation of random diagonal sums of Bernoulli matrices

We use the Stein-Chen method to prove new explicit inequalities for the total variation, Wasserstein and local distances between the distribution of a random diagonal sum of a Bernoulli matrix and a Poisson distribution. Approximation results using a finite signed measure of higher order are given as well. Some of our bounds improve on those in Theorem 4.A of A.D. Barbour, L. Holst and S. Janson (Poisson approximation. Clarendon Press, Oxford, 1992).