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Pré-Publication, Document De Travail Année : 2014

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

Résumé

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 trans-form 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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Dates et versions

hal-01097276 , version 1 (24-12-2014)
hal-01097276 , version 2 (04-03-2016)
hal-01097276 , version 3 (15-01-2021)
hal-01097276 , version 4 (14-12-2021)

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  • HAL Id : hal-01097276 , version 1

Citer

Thierry Klein, A Lagnoux, P Petit. A conditional Berry-Esseen bound and a conditional large deviation result without Laplace transform. Application to hashing with linear probing. 2014. ⟨hal-01097276v1⟩
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