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29 March 2024
 
  » arxiv » 0801.2115

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A study of counts of Bernoulli strings via conditional Poisson processes
Fred W. Huffer ; Jayaram Sethuraman ; Sunder Sethuraman ;
Date 14 Jan 2008
AbstractWe say that a string of length $d$ occurs, in a Bernoulli sequence, if a success is followed by exactly $(d-1)$ failures before the next success. The counts of such $d$-strings are of interest, and in specific independent Bernoulli sequences are known to correspond to asymptotic $d$-cycle counts in random permutations.
In this note, we give a new framework, in terms of conditional Poisson processes, which allows for a quick characterization of the joint distribution of the counts of all $d$-strings, in a general class of Bernoulli sequences, as certain mixtures of the product of Poisson measures. This general class includes all Bernoulli sequences considered before, as well many new sequences.
Source arXiv, 0801.2115
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