Talk by David Levin (University of Oregon)
Date and Time: Thursday, October 23, 2008, 10:00 AM in AP&M 6402.
Title: Mixing of mean-field Glauber Dynamics
Abstract:
I will describe the three phases for the mixing time (the time to
equilibriate) of the Glauber dynamics for the Ising model on the
complete graph on n vertices. At high temperature, the time required to mix
is order n(log n), and there is a cut-off, meaning that in a window
of order n, the distance to equilibrium drops from near one
to near zero. At critical temperature, the dynamics mix in
order n^(3/2) steps. At low temperature, the mixing is exponentially
slow, but if the dynamics are restricted to one of the two
modes of the stationary distribution, then it mixes in order
n(log n) steps. Joint work with M. Luczak and Y. Peres.