Séminaire Lotharingien de Combinatoire, 84B.69 (2020), 12 pp.

Subhajit Ghosh

Cutoff for the Warp-Transpose Top with Random Shuffle

Abstract. 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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