On finite range stable type concentration

Abstract

The purpose of these notes is to further complete our understanding of the stable concentration phenomenon, by obtaining the finite range behavior of $P(F-E[F]\ge x)$, with $F=f(X)$ where $f$ is a Lipschitz function and $X$ is a stable random vector or with $F$ a stochastic functional on the Poisson space equipped with a stable Lévy measure.

24 pages