The model we study belongs to a wide class of Markov processes called strings of characters. The model consists of a transient random walk on integers which write and re-write letters (characters) from some finite alphabet on its location. We apply the precise asymptotic theorems established for compound semi-Markov renewal process (CSRP) to study the asymptotics of the statistics of frozen characters, that is the characters on the integers that never will be visited again after some (increasing) time.

Original languageEnglish
Pages (from-to)885-899
Number of pages15
JournalMarkov Processes And Related Fields
Issue number5
Publication statusPublished - 2020


  • compound semi-Markov renewal process (CSRP)
  • large deviation principle
  • normal deviations
  • moderate deviation


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