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Maximum Waiting Times are Asymptotically Independent

Published online by Cambridge University Press:  12 September 2008

Tamás F. Móri
Tamás F. Móri
Affiliation:
Department of Probability Theory and Statistics, Eötvös Loránd University, H-1088 Budapest
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Abstract

For every n consider a subset Hn of the patterns of length n over a fixed finite alphabet. The limit distribution of the waiting time until each element of Hn appears in an infinite sequence of independent, uniformly distributed random letters was determined in an earlier paper. This time we prove that these waiting times are getting independent as n → ∞. Our result is used for applying the converse part of the Borel–Cantelli lemma to problems connected with such waiting times, yielding thus improvements on some known theorems.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 1 , Issue 3 , September 1992 , pp. 251 - 264
Copyright
Copyright © Cambridge University Press 1992

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