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Glauber Dynamics of colorings on treesMathematical Physics & Probability
|Speaker: ||Yumeng Zhang, UC Berkeley|
|Location: ||1147 MSB|
|Start time: ||Wed, Feb 4 2015, 4:10PM|
The mixing time of the Glauber dynamics for spin systems on trees is closely related to reconstruction problem. Martinelli, Sinclair and Weitz established this correspondence for a class of spin systems with soft constraints bounding
the log-Sobolev constant by a comparison with the block dynamics. However, when there are hard constraints, the block dynamics may be reducible.
We introduce a variant of the block dynamics extending these results to a wide class of spin systems with hard constraints. This applies for essentially any spin system that has non-reconstruction provided that on average the root
is not locally frozen in a large neighborhood. In particular we prove that the mixing time of the Glauber dynamics for colorings on the regular tree is $O(n\log n)$ in the entire known non-reconstruction regime.