Sub-exponential tail bounds for conditioned stable Bienaymé-Galton-Watson trees

Abstract

We establish uniform sub-exponential tail bounds for the width, height and maximal outdegree of critical Bienaymé-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.

34 pages, 1 figure. Final version: to appear in Probab. Theory Related Fields

References in corpus (3)

• Random stable looptrees
• A simple proof of Duquesne's theorem on contour processes of conditioned Galton-Watson trees
• Percolation on random triangulations and stable looptrees