The Annals of Applied Probability

Analysis of top-swap shuffling for genome rearrangements

Nayantara Bhatnagar, Pietro Caputo, Prasad Tetali, and Eric Vigoda

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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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Ann. Appl. Probab., Volume 17, Number 4 (2007), 1424-1445.

First available in Project Euclid: 10 August 2007

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Zentralblatt MATH identifier

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 92D10: Genetics {For genetic algebras, see 17D92}

Card shuffling genome rearrangement random transpositions relaxation time


Bhatnagar, Nayantara; Caputo, Pietro; Tetali, Prasad; Vigoda, Eric. Analysis of top-swap shuffling for genome rearrangements. Ann. Appl. Probab. 17 (2007), no. 4, 1424--1445. doi:10.1214/105051607000000177.

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