Juan Vera

Phase Transition for the Mixing Time of the Glauber Dynamics for
Coloring Regular Trees

We prove that the mixing time of the Glauber dynamics for random
k-colorings of the complete tree with branching factor b undergoes a
phase transition at k = b(1 + o_b(1))/ ln b.  Our main result shows
nearly sharp bounds on the mixing time of the dynamics on the complete
tree with n vertices for k = Cb/ ln b colors with constant C. The
critical point C = 1 is interesting since it coincides (at least up to
first order) to the so-called reconstruction threshold. The
reconstruction threshold has been of considerable interest recently
since it appears to have close connections to the efficiency of
certain local algorithms, and this work was inspired by our attempt to
understand these connections in this particular setting.


Join work with Prasad Tetali, Eric Vigoda and Linji Yang