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August 2007 Analysis of top-swap shuffling for genome rearrangements
Nayantara Bhatnagar, Pietro Caputo, Prasad Tetali, Eric Vigoda
Ann. Appl. Probab. 17(4): 1424-1445 (August 2007). DOI: 10.1214/105051607000000177

Abstract

We study Markov chains which model genome rearrangements. These models are useful for studying the equilibrium distribution of chromosomal lengths, and are used in methods for estimating genomic distances. The primary Markov chain studied in this paper is the top-swap Markov chain. The top-swap chain is a card-shuffling process with n cards divided over k decks, where the cards are ordered within each deck. A transition consists of choosing a random pair of cards, and if the cards lie in different decks, we cut each deck at the chosen card and exchange the tops of the two decks. We prove precise bounds on the relaxation time (inverse spectral gap) of the top-swap chain. In particular, we prove the relaxation time is Θ(n+k). This resolves an open question of Durrett.

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Nayantara Bhatnagar. Pietro Caputo. Prasad Tetali. Eric Vigoda. "Analysis of top-swap shuffling for genome rearrangements." Ann. Appl. Probab. 17 (4) 1424 - 1445, August 2007. https://doi.org/10.1214/105051607000000177

Information

Published: August 2007
First available in Project Euclid: 10 August 2007

zbMATH: 1135.92024
MathSciNet: MR2344312
Digital Object Identifier: 10.1214/105051607000000177

Subjects:
Primary: 60J27
Secondary: 92D10

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.17 • No. 4 • August 2007
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