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April, 1988 Maximal Length of Common Words Among Random Letter Sequences
Samuel Karlin, Friedemann Ost
Ann. Probab. 16(2): 535-563 (April, 1988). DOI: 10.1214/aop/1176991772


Consider random letter sequences $\{\xi^{(\sigma)}_t, t = 1,\ldots, N; \sigma = 1,\ldots, s\}$ based on a finite alphabet generated by uniformly mixing stationary processes. The asymptotic distributional properties of the length of the longest common word in $r$ or more of the $s$ sequences $K_{r,s}(N)$, are investigated. When the probability measures of the different sequences are not too dissimilar, a classical extremal type limit law holds for $K_{r,s}(N) - (r \log N/(-\log \lambda)), \lambda$ being an appropriate local match parameter. The distributional properties of other long-word relationships and patterns among the sequences are also discussed.


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Samuel Karlin. Friedemann Ost. "Maximal Length of Common Words Among Random Letter Sequences." Ann. Probab. 16 (2) 535 - 563, April, 1988.


Published: April, 1988
First available in Project Euclid: 19 April 2007

zbMATH: 0645.60034
MathSciNet: MR929062
Digital Object Identifier: 10.1214/aop/1176991772

Primary: 60F10
Secondary: 60F99

Keywords: extremal distributions , local match distribution , longest common word , Random letter sequences , uniformly mixing stationary processes

Rights: Copyright © 1988 Institute of Mathematical Statistics

Vol.16 • No. 2 • April, 1988
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