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arXiv · 0907.5137

Standard deviation of the longest common subsequence

Jüri Lember·Heinrich Matzinger
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Abstract

Let $L_n$ be the length of the longest common subsequence of two independent i.i.d. sequences of Bernoulli variables of length $n$. We prove that the order of the standard deviation of $L_n$ is $\sqrt{n}$, provided the parameter of the Bernoulli variables is small enough. This validates Waterman's conjecture in this situation [Philos. Trans. R. Soc. Lond. Ser. B 344 (1994) 383--390]. The order conjectured by Chvatal and Sankoff [J. Appl. Probab. 12 (1975) 306--315], however, is different.

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Jüri Lember, Heinrich Matzinger. 2009-07-29. Standard deviation of the longest common subsequence. https://doi.org/10.1214/08-aop436

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