Connections between bernoulli strings and random permutations

Jayaram Sethuraman, Sunder Sethuraman

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)

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 publicationtThe Legacy of Alladi Ramakrishnan in the Mathematical Sciences
PublisherSpringer New York
Pages389-399
Number of pages11
ISBN (Print)9781441962621
DOIs
StatePublished - 2010
Externally publishedYes

Fingerprint

Random Permutation
Bernoulli
Count
Strings
Record Values
Bayesian Nonparametrics
Poisson process
Joint Distribution
Open Problems
Random variable
Cycle

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 tThe 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

Connections between bernoulli strings and random permutations. / Sethuraman, Jayaram; Sethuraman, Sunder.

tThe Legacy of Alladi Ramakrishnan in the Mathematical Sciences. Springer New York, 2010. p. 389-399.

Research output: Chapter in Book/Report/Conference proceedingChapter

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