STRING MATCHING - THE ERGODIC CASE

Of interest in DNA analysis is the length L(x1n) of the longest sequence that appears twice in a sequence x1n 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(x1n) = 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).