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Contributions of Alladi Ramakrishnan to the Mathematical Sciences Read chapter Read first chapter

2010 | OriginalPaper | Chapter

Connections Between Bernoulli Strings and Random Permutations

Authors : Jayaram Sethuraman, Sunder Sethuraman

Published in: The Legacy of Alladi Ramakrishnan in the Mathematical Sciences

Publisher: Springer New York

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Summary

A sequence of random variables, each taking only two values “0” or “1,” is called a Bernoulli sequence. Consider the counts of occurrences of strings of the form {11}, {101}, {1001}, … in Bernoulli sequences. Counts of such Bernoulli strings arise in the study of the cycle structure of random permutations, Bayesian nonparametrics, record values etc. The joint distribution of such counts is a problem worked on by several researchers. In this paper, we summarize the recent technique of using conditional marked Poisson processes which allows to treat all cases studied previously. We also give some related open problems.

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previous chapter Optimal Weights for a Class of Rank Tests for Censored Bivariate Data
next chapter Storage Models for a Class of Master Equations with Separable Kernels
Footnotes
1
Research partially supported by ARO-W911NF-09-1-0338† and NSF-DMS 0906713∗. Approved for public release, distribution unlimited. Research partially suported by ARO-W911NF-09-1-0338† and NSF-DMS 0906713∗. Approved for public release, distribution unlimited.
 
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Metadata
Title
Connections Between Bernoulli Strings and Random Permutations
Authors
Jayaram Sethuraman
Sunder Sethuraman
Copyright Year
2010
Publisher
Springer New York
Book
The Legacy of Alladi Ramakrishnan in the Mathematical Sciences

Print ISBN: 978-1-4419-6262-1

Electronic ISBN: 978-1-4419-6263-8

Copyright Year: 2010

DOI
https://doi.org/10.1007/978-1-4419-6263-8_24

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