## The Annals of Probability

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

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

Samuel Karlin and Friedemann Ost

#### 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

**Permanent link to this document**

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**

links.jstor.org

**Subjects**

Primary: 60F10: Large deviations

Secondary: 60F99: None of the above, but in this section

**Keywords**

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

#### 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