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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
*G*_{n} wreath *S*_{n} generated by the elements of the forms (*e*,...,*e*,*g*;id) and
(*e*,...,*e*,*g*^{-1},*e*,...,*e*,*g*;(*i*,*n*)) for *g* in *G*_{n}, 1<=*i*<*n*. We call this the warp-transpose top with random shuffle on
*G*_{n} wreath *S*_{n}. We find the spectrum of the transition probability matrix for this shuffle. We prove that the mixing time for this shuffle is of order
*n*log(*n*)+(1/2)*n*log(|*G*_{n}|-1) and under some condition on |*G*_{n}|, this shuffle exhibits the cutoff phenomenon.

Received: November 20, 2019.
Accepted: February 20, 2020.
Final version: April 30, 2020.

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