Total variation cutoff for the transpose top-2 with random shuffle

Seminar
Speaker
Subhajit Ghosh (BIU)
Date
19/12/2021 - 15:30 - 14:05Add to Calendar 2021-12-19 14:05:00 2021-12-19 15:30:00 Total variation cutoff for the transpose top-2 with random shuffle In this talk, we focus on the properties of a random walk on the alternating group $A_n$ generated by $3$-cycles of the form $(i,n-1,n)$ and $(i,n,n-1)$. We call this the transpose top-$2$ with random shuffle. We find the spectrum of the transition matrix of this shuffle. We show that the mixing time is of order $\left(n-\frac{3}{2}\right)\log n$ and prove that there is a total variation cutoff for this shuffle. zoom אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
zoom
Abstract

In this talk, we focus on the properties of a random walk on the alternating group $A_n$ generated by $3$-cycles of the form $(i,n-1,n)$ and $(i,n,n-1)$. We call this the transpose top-$2$ with random shuffle. We find the spectrum of the transition matrix of this shuffle. We show that the mixing time is of order $\left(n-\frac{3}{2}\right)\log n$ and prove that there is a total variation cutoff for this shuffle.

תאריך עדכון אחרון : 16/12/2021