## “Local central limit theorem and potential kernel estimates for a class of symmetric heavy-tailed random variables”

Venerdì 9 Luglio 2021, ore 14:30 - Zoom - Wioletta Ruzsel (University of Utrecht)

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 $\mathbb{Z}$ in the domain of attraction of an $\alpha$-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.