Analysis of top-swap shuffling for genome rearrangements
Nayantara Bhatnagar, Pietro Caputo, Prasad Tetali, and Eric Vigoda
Source: Ann. Appl. Probab.
Volume 17, Number 4
(2007), 1424-1445.
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.
Primary Subjects: 60J27
Secondary Subjects: 92D10
Keywords: Card shuffling; genome rearrangement; random transpositions; relaxation time
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aoap/1186755245
Digital Object Identifier: doi:10.1214/105051607000000177
Mathematical Reviews number (MathSciNet):
MR2344312
Zentralblatt MATH identifier:
1135.92024
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