### Abstract

We analyze sequences of letters on a ring. Our objective is to determine the statistics of the occurrences of a set of r-letter words when the sequence is chosen as a periodic Markov chain of order ≤ r - 1. We first obtain a generating function for the associated probability distribution and then display its Poisson limit. For an i.i.d. letter sequence, correction terms to the Poisson limit are given. Finally, we indicate how a hidden Markov chain fits into this scheme.

Original language | English (US) |
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Pages (from-to) | 145-160 |

Number of pages | 16 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 59 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2006 |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Percus, J. K., & Percus, O. E. (2006). The statistics of words on rings.

*Communications on Pure and Applied Mathematics*,*59*(1), 145-160. https://doi.org/10.1002/cpa.20096