[Probability] Statistical Mechanics Seminar, Thursday 2pm MS.04
D.Ueltschi at warwick.ac.uk
Tue May 18 15:03:15 BST 2010
We have a statistical mechanics seminar this Thursday (18.05.2010), 2pm in MS.04.
Speaker: Nathanaël Berestycki (University of Cambridge)
Emergence of giant cycles in random transpositions: a new proof of a result of Oded Schramm
Consider the permutation-valued process obtained by performing random transpositions at rate 1, started from the identity permutation. In 2005 Oded Schramm proved a beautiful result, conjectured by David Aldous, that the distribution of large cycle sizes has Poisson-Dirichlet asymptotics after (1+eps)n/2 steps. In particular this is also the time for emergence of giant cycles. I will present a very short and non-computational proof of this fact, which can also be generalised to some other models. I will discuss related conjectures and ideas, and (time-permitting) explain briefly how this is connected to a problem on mixing times of random walks (this last bit being joint work with Oded Schramm and Ofer Zeitouni).
The program for the rest of the term can be found on the web page
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