Sub-exponential tail bounds for conditioned stable Bienaym\'e-Galton-Watson trees

Abstract

We establish uniform sub-exponential tail bounds for the width, height and maximal outdegree of critical Bienaym\'e-Galton-Watson trees conditioned on having a large fixed size, whose offspring distribution belongs to the domain of attraction of a stable law. This extends results obtained for the height and width by Addario-Berry, Devroye & Janson in the finite variance case.