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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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.

Article information

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

Dates
First available in Project Euclid: 10 August 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1186755245

Digital Object Identifier
doi:10.1214/105051607000000177

Mathematical Reviews number (MathSciNet)
MR2344312

Zentralblatt MATH identifier
1135.92024

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

Keywords
Card shuffling genome rearrangement random transpositions relaxation time

Citation

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. https://projecteuclid.org/euclid.aoap/1186755245


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References

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