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May 2009 Standard deviation of the longest common subsequence
Jüri Lember, Heinrich Matzinger
Ann. Probab. 37(3): 1192-1235 (May 2009). DOI: 10.1214/08-AOP436

Abstract

Let Ln 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 Ln 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.

Citation

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Jüri Lember. Heinrich Matzinger. "Standard deviation of the longest common subsequence." Ann. Probab. 37 (3) 1192 - 1235, May 2009. https://doi.org/10.1214/08-AOP436

Information

Published: May 2009
First available in Project Euclid: 19 June 2009

zbMATH: 1182.60004
MathSciNet: MR2537552
Digital Object Identifier: 10.1214/08-AOP436

Subjects:
Primary: 41A25, 60K35
Secondary: 60C05C

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 3 • May 2009
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