English

Deviation results for sparse tables in hashing with linear probing

Probability 2021-12-16 v3

Abstract

We consider the model of hashing with linear probing and we establish the moderate and large deviations for the total displacement in sparse tables. In this context, Weibull-like-tailed random variables appear. Deviations for sums of such heavy-tailed random variables are studied in \cite{Nagaev69-1,Nagaev69-2}. Here we adapt the proofs therein to deal with conditioned sums of such variables and solve the open question in \cite{TFC12}. By the way, we establish the deviations of the total displacement in full tables, which can be derived from the deviations of empirical processes of i.i.d.\ random variables established in \cite{Wu94}..

Keywords

Cite

@article{arxiv.1603.02235,
  title  = {Deviation results for sparse tables in hashing with linear probing},
  author = {Thierry Klein and A Lagnoux and P Petit},
  journal= {arXiv preprint arXiv:1603.02235},
  year   = {2021}
}
R2 v1 2026-06-22T13:05:38.445Z