A conditional Berry-Esseen bound and a conditional large deviation result without Laplace transform. Application to hashing with linear probing

Thierry Klein; Agnès Lagnoux; Pierre Petit

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arXiv · 1503.08848

A conditional Berry-Esseen bound and a conditional large deviation result without Laplace transform. Application to hashing with linear probing

Thierry Klein·Agnès Lagnoux·Pierre Petit

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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.

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Thierry Klein, Agnès Lagnoux, Pierre Petit. 2015-03-30. A conditional Berry-Esseen bound and a conditional large deviation result without Laplace transform. Application to hashing with linear probing. https://arxiv.org/abs/1503.08848

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