Dear Colleagues, We would like to invite you to the following Probability seminar that will take place on July 9 at 14.30 by the zoom platform. ________________________________________________________ Speaker: Wioletta Ruszel (University of Utrecht) Title: Local central limit theorem and potential kernel estimates for a class of symmetric heavy-tailed random variables. 09 JULY (Friday) - 14:30 zoom link: TBA available on the webpage https://www.math.unipd.it/~bianchi/seminari/ ) Abstract: In this talk we will discuss stable local limit theorems and potential kernel estimates. In particular we consider a class of heavy-tailed random variables on Z in the domain of attraction of an -stable random variable of index \alpha \in (0, 2) satisfying a certain expansion of their characteristic function expansion. Our results include sharp convergence rates for the local (stable) central limit theorem, a detailed expansion of the characteristic function of a long-range random walk with transition and detailed asymptotic estimates of the discrete potential kernel. This is joint work with Leandro Chiarini (UU) and Milton Jara (IMPA) and is based on arXiv.com/2101.01609. -- Alessandra Bianchi Dip. di Matematica Università di Padova Via Trieste, 63 - 35121 Padova, Italy phone: +39 049 827 14 06 fax: +39 049 827 14 28 e-mail: bianchi@math.unipd.it http://www.math.unipd.it/~bianchi/