A conditional Berry-Esseen bound and a conditional large deviation result without Laplace transform. Application to hashing with linear probing
Probability
2015-04-01 v1
Abstract
\noindent We study the asymptotic behavior of a sum of independent and identically distributed random variables conditioned by a sum of independent and identically distributed integer-valued random variables. We prove a Berry-Esseen bound in a general setting and a large deviation result when the Laplace transform of the underlying distribution is not defined in a neighborhood of zero. Then we present several combinatorial applications. In particular, we prove a large deviation result for the model of hashing with linear probing.
Cite
@article{arxiv.1503.08848,
title = {A conditional Berry-Esseen bound and a conditional large deviation result without Laplace transform. Application to hashing with linear probing},
author = {Thierry Klein and Agnès Lagnoux and Pierre Petit},
journal= {arXiv preprint arXiv:1503.08848},
year = {2015}
}