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math.PR2004★ 11 cited
The hyperbolic geometry of random transpositions
Nathanaël Berestycki
Turn the set of permutations of objects into a graph by connecting two permutations that differ by one transposition, and let be the simple random walk on this grap…
math.PR2004
A phase transition in the random transposition random walk
Nathanael Berestycki, Rick Durrett
Our work is motivated by Bourque and Pevzner's (2002) simulation study of the effectiveness of the parsimony method in studying genome rearrangement, and leads to a surprising resu…