Total variation cutoff for the flip-transpose top with random shuffle

Abstract: We consider a random walk on the hyperoctahedral group $B_n$ generated by the signed permutations of the form $(i,n)$ and $(-i,n)$ for $1\leq i\leq n$. We call this the \emph{flip-transpose top with random shuffle} on $B_n$. We find the spectrum of the transition probability matrix for this shuffle. We prove that this shuffle exhibits the total variation cutoff phenomenon with cutoff time $n\log n$. We also show that a biased variant of this shuffle exhibits the total variation cutoff with the same cutoff time.

probability

Audience: advanced learners

Bangalore Probability Seminar

Series comments: The link to zoom meeting can be found on the seminar's google calendar - www.isibang.ac.in/~d.yogesh/BPS.html