Seminar Event Detail

Colloquium Series

Date:  Tuesday, September 28, 2021
Location:  1360 East Hall (4:00 PM to 5:00 PM)

Title:  Spectral techniques in Markov chain mixing

Abstract:   How many steps does it take to shuffle a deck of n cards, if at each step we pick two cards uniformly at random and swap them? Diaconis and Shahshahani proved that 1/2 n log n steps are necessary and sufficient to mix the deck. Using the representation theory of the symmetric group, they proved that this random transpositions card shuffle exhibits a sharp transition from being unshuffled to being very well shuffled. This is called the cutoff phenomenon. In this talk, I will explain how to use the spectral information of a Markov chain to study cutoff. As an application, I will briefly discuss the random to random card shuffle (joint with M. Bernstein) and the non-backtracking random walk on Ramanujan graphs (joint with P. Sarnak).


Speaker:  Evita Nestoridi
Institution:  Princeton University

Event Organizer:     


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