Connections between bernoulli strings and random permutations

Jayaram Sethuraman; Sunder Sethuraman

doi:10.1007/978-1-4419-6263-8_24

Connections between bernoulli strings and random permutations

Jayaram Sethuraman, Sunder Sethuraman

Research output: Chapter in Book/Report/Conference proceeding › Chapter

2 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 language	English (US)
Title of host publication	The Legacy of Alladi Ramakrishnan in the Mathematical Sciences
Publisher	Springer New York
Pages	389-399
Number of pages	11
ISBN (Print)	9781441962621
DOIs	https://doi.org/10.1007/978-1-4419-6263-8_24
State	Published - 2010
Externally published	Yes

Keywords

Bernoulli
Cycles
Nonhomogeneous
Poisson processes
Random permutations
Records
Spacings
Strings

ASJC Scopus subject areas

General Mathematics

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10.1007/978-1-4419-6263-8_24

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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.",

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AU - Sethuraman, Sunder

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AB - 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.

KW - Bernoulli

KW - Cycles

KW - Nonhomogeneous

KW - Poisson processes

KW - Random permutations

KW - Records

KW - Spacings

KW - Strings

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EP - 399

BT - The Legacy of Alladi Ramakrishnan in the Mathematical Sciences

PB - Springer New York

ER -

Connections between bernoulli strings and random permutations

Abstract

Keywords

ASJC Scopus subject areas

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