### Cutoff for the random to random shuffle

- Series
- ACO Student Seminar
- Time
- Friday, April 28, 2017 - 13:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Megan Bernstein – School of Mathematics, Georgia Tech

The random to random shuffle on a deck of cards is given by at each
step choosing a random card from the deck, removing it, and replacing it
in a random location. We show an upper bound for the total variation
mixing time of the walk of 3/4n log(n) +cn steps. Together with matching
lower bound of Subag (2013), this shows the walk mixes with cutoff at
3/4n log(n) steps, answering a conjecture of Diaconis. We use the
diagonalization of the walk by Dieker and Saliola (2015), which relates
the eigenvalues to Young tableaux.
Joint work with Evita Nestorid.