Séminaire Lotharingien de Combinatoire, 84B.69 (2020), 12 pp.
Cutoff for the Warp-Transpose Top with Random Shuffle
We consider a random walk on the complete monomial group
Gn wreath Sn generated by the elements of the forms (e,...,e,g;id) and
(e,...,e,g-1,e,...,e,g;(i,n)) for g in Gn, 1<=i<n. We call this the warp-transpose top with random shuffle on
Gn wreath Sn. We find the spectrum of the transition probability matrix for this shuffle. We prove that the mixing time for this shuffle is of order
nlog(n)+(1/2)nlog(|Gn|-1) and under some condition on |Gn|, this shuffle exhibits the cutoff phenomenon.
Received: November 20, 2019.
Accepted: February 20, 2020.
Final version: April 30, 2020.
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