Gaps in discrete random samples

Speaker(s)

Paweł Hitczenko

Affiliation

Drexel University

Date

Dec. 6, 2012, 12:15 p.m.

Room

room 3260

Seminar

Seminar of Probability Group

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For a sequence of independent and identically distributed random variables with values in the set of non-negative integers we investigate the number of gaps and the length of the longest gap in the set of the first n values. We obtain necessary and sufficient conditions in terms of the tail sequence for the gaps to vanish asymptotically (almost surely or in probability) as n goes to infinity.

We also give a sufficient condition for  the length of the longest gap to tend to infinity in probability.

This is based on a joint work with Rudolf Gruebel from Leibniz Universitaet Hannover.

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