Open Access
July, 1992 String Matching: The Ergodic Case
Paul C. Shields
Ann. Probab. 20(3): 1199-1203 (July, 1992). DOI: 10.1214/aop/1176989686


Of interest in DNA analysis is the length $L(x^n_1)$ of the longest sequence that appears twice in a sequence $x^n_1$ of length $n$. Karlin and Ghandour and Arratia and Waterman have shown that if the sequence is a sample path from an i.i.d. or Markov process, then $L(x^n_1) = O(\log n)$. In this paper, examples of ergodic processes are constructed for which the asymptotic growth rate is infinitely often as large as $\lambda(n)$, where $\lambda(n)$ is subject only to the condition that it be $o(n)$.


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Paul C. Shields. "String Matching: The Ergodic Case." Ann. Probab. 20 (3) 1199 - 1203, July, 1992.


Published: July, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0753.92021
MathSciNet: MR1175257
Digital Object Identifier: 10.1214/aop/1176989686

Primary: 92A10
Secondary: 60F15

Keywords: Entropy , string matching

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.20 • No. 3 • July, 1992
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