The statistics of words on rings

Jerome K. Percus, Ora E. Percus

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)145-160
Number of pages16
JournalCommunications on Pure and Applied Mathematics
Issue number1
StatePublished - Jan 2006

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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