Sub-exponential tail bounds for conditioned stable Bienaym\'e-Galton-Watson trees
Probability
2018-02-19 v2
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.
Cite
@article{arxiv.1504.04358,
title = {Sub-exponential tail bounds for conditioned stable Bienaym\'e-Galton-Watson trees},
author = {Igor Kortchemski},
journal= {arXiv preprint arXiv:1504.04358},
year = {2018}
}
Comments
34 pages, 1 figure. Final version: to appear in Probab. Theory Related Fields