Brandeis-Harvard-MIT-Northeastern Joint Mathematics Colloquium

Friday, October 22, 2021 at 4:30pm to 6:00pm

MIT, 2-190 77 Massachusetts Avenue, Cambridge, MA 02139

Speaker:   Evita Nestoridi (Princeton University)

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 $\frac{1}{2} n log n$ 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).

Register here.

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For more information please go to https://colloquium.sites.northeastern.edu/.

Event Type

Conferences/Seminars/Lectures

Events By Interest

Academic

Events By Audience

Public, MIT Community, Students, Alumni, Faculty, Staff

Events By School

School of Science

Tags

MIT Mathematics, Scott Sheffield, Seminars at MIT

Website

http://www.northeastern.edu/tzhou/bhm...

Department
Department of Mathematics
Hashtag

#MIT Math

Contact Email

rzammuto@mit.edu

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