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A Conditional Berry-esseen Bound And A Conditional Large Deviation Result Without Laplace Transform. Application To Hashing With Linear Probing

Klein Thierry, Lagnoux Agnès, Petit Pierre. Arxiv 2015

[Paper]    
ARXIV Independent

\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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