Deviation results for sparse tables in hashing with linear probing

Thierry Klein (1) , A Lagnoux (1) , P Petit (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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}..

Mots clés: large deviations; hashing with linear probing; parking problem; Airy distribution; {\L}ukasiewicz random walk; empirical processes; conditioned sums of i.i.d.\ random variables; triangular arrays; Weibull-like distribution

Domaines: Probabilités [math.PR]

Thierry Klein, A Lagnoux, P Petit. Deviation results for sparse tables in hashing with linear probing. 2014. ⟨hal-01097276v2⟩