|COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring.|
On the mixing time of random conjugacy walks
If you have a question about this talk, please contact Julia Blackwell.
Let G be a finite graph and consider a random walk on this graph. How long does it take for this walk to be well mixed, i.e., to be close to its equilibrium distribution? A striking phenomenon, discovered in the early 80’s by Aldous and Diaconis independently, is that convergence to equilibrium often occurs abruptly: this is known as the cutoff phenomenon. In this talk we shall consider the classical example of random transpositions over the symmetric group. In this case, Diaconis and Shahshahani used representation theory to prove that such a cutoff occurs at time (1/2) n log n. We present a new, probabilistic proof of this result, which extends readily to other walks where the step distribution is uniform over a given conjugacy class. This proves a conjecture of Roichman (1996) that the mixing time of this process is (1/C) n log n, where C is the size of the conjugacy class. This is joint work with Oded Schramm and Ofer Zeitouni
This talk is part of the Probability series.
This talk is included in these lists:
Note that ex-directory lists are not shown.
Other listsCRASSH Automating Biology using Robot Scientists British Society of Aesthetics Cambridge Lecture Series
Other talksLARMOR LECTURE - The statistical physics of stem cell biology: Dicing with fate The cause of all our troubles: the American invention of isolationism in World War II Transcriptional regulation and downstream program of Hox and Cdx genes during axial development in the mouse embryo. CERF Cavalcade Commuting the mean-field and classical limits in quantum mechanic The realization of large arrays of quantum dots via a multiplexed charge-locking system (SP Workshop)