Deviation results for sparse tables in hashing with linear probing
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
parking problem
hashing with linear probing
large deviations
Airy distribution
{\L}ukasiewicz random walk
empirical processes
conditioned sums of i.i.d.\ random variables
triangular arrays
Weibull-like distribution
parking problem
Brownian motion
Łukasiewicz random walk
conditioned sums of i.i.d. random variables
Weibull-like distribution AMS subject classification: 60F10
60C05
60G50
68W40
Origin : Files produced by the author(s)
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