## The Annals of Probability

### Maximal Length of Common Words Among Random Letter Sequences

#### Abstract

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.

#### Article information

Source
Ann. Probab., Volume 16, Number 2 (1988), 535-563.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176991772

Digital Object Identifier
doi:10.1214/aop/1176991772

Mathematical Reviews number (MathSciNet)
MR929062

Zentralblatt MATH identifier
0645.60034

JSTOR

Subjects
Primary: 60F10: Large deviations
Secondary: 60F99: None of the above, but in this section

#### Citation

Karlin, Samuel; Ost, Friedemann. Maximal Length of Common Words Among Random Letter Sequences. Ann. Probab. 16 (1988), no. 2, 535--563. doi:10.1214/aop/1176991772. https://projecteuclid.org/euclid.aop/1176991772