Office of Scientific and International Cooperation

Abstract: In this talk I will introduce the so-called mod-Poisson approximation schemes to obtain asymptotic and non asymptotic results in the context of Poisson approximation for various distances. The results rely on simple facts from the theory of absolutely convergent Fourier series on the torus (the Wiener algebra) and basic facts from the algebra of symmetric functions. We shall focus on applications of our results to some classical problems in probabilistic number theory and to random permutations. If time allows we shall discuss how these ideas can also be numerically implemented in some applied math problems such as credit risk portfolio losses.