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November, 1995 A Limit Theorem for Matching Random Sequences Allowing Deletions
Yu Zhang
Ann. Appl. Probab. 5(4): 1236-1240 (November, 1995). DOI: 10.1214/aoap/1177004613

Abstract

We consider a sequence matching problem involving the optimal alignment score for contiguous sequences, rewarding matches by one unit and penalizing for deletions and mismatches by parameters $\delta$ and $\mu$, respectively. Let $M_n$ be the optimal score over all possible choices of two contiguous regions. Arratia and Waterman conjectured that, when the score constant $a(\mu, \delta) < 0$, $P\big(\frac{M_n}{\log n} \rightarrow 2b\big) = 1$ for some constant $b$. Here we prove the conjecture affirmatively.

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Yu Zhang. "A Limit Theorem for Matching Random Sequences Allowing Deletions." Ann. Appl. Probab. 5 (4) 1236 - 1240, November, 1995. https://doi.org/10.1214/aoap/1177004613

Information

Published: November, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0855.62012
MathSciNet: MR1384373
Digital Object Identifier: 10.1214/aoap/1177004613

Subjects:
Primary: 62E20
Secondary: 62P10

Keywords: Sequence matching

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.5 • No. 4 • November, 1995
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