### 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 | tThe Legacy of Alladi Ramakrishnan in the Mathematical Sciences |

Publisher | Springer New York |

Pages | 389-399 |

Number of pages | 11 |

ISBN (Print) | 9781441962621 |

DOIs | |

State | Published - 2010 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*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.

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

*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

}

TY - CHAP

T1 - Connections between bernoulli strings and random permutations

AU - Sethuraman, Jayaram

AU - Sethuraman, Sunder

PY - 2010

Y1 - 2010

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=84890170162&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84890170162&partnerID=8YFLogxK

U2 - 10.1007/978-1-4419-6263-8_24

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

M3 - Chapter

AN - SCOPUS:84890170162

SN - 9781441962621

SP - 389

EP - 399

BT - tThe Legacy of Alladi Ramakrishnan in the Mathematical Sciences

PB - Springer New York

ER -