Connections between bernoulli strings and random permutations

Jayaram Sethuraman, Sunder Sethuraman

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations

Abstract

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.

Original languageEnglish (US)
Title of host publicationThe Legacy of Alladi Ramakrishnan in the Mathematical Sciences
PublisherSpringer New York
Pages389-399
Number of pages11
ISBN (Print)9781441962621
DOIs
StatePublished - Jan 1 2010
Externally publishedYes

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Keywords

  • Bernoulli
  • Cycles
  • Nonhomogeneous
  • Poisson processes
  • Random permutations
  • Records
  • Spacings
  • Strings

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Sethuraman, J., & Sethuraman, S. (2010). Connections between bernoulli strings and random permutations. In The Legacy of Alladi Ramakrishnan in the Mathematical Sciences (pp. 389-399). Springer New York. https://doi.org/10.1007/978-1-4419-6263-8_24