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The statistics of words on rings
Author(s) -
Percus Jerome K.,
Percus Ora E.
Publication year - 2006
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20096
Subject(s) - mathematics , markov chain , poisson distribution , sequence (biology) , limit (mathematics) , statistics , order statistic , set (abstract data type) , generating function , combinatorics , discrete mathematics , mathematical analysis , computer science , genetics , biology , programming language
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. © 2005 Wiley Periodicals, Inc.