Extremality of Gibbs measure for colorings on trees
Seminar Room 1, Newton Institute
We consider the problem of extremality of the free boundary Gibbs measure for k-colorings on the tree of branching factor D. Extremality of the measure is equivalent to reconstruction non-solvability, that is, in expectation, over random colorings of the leaves, the conditional probability at the root for any color tends to 1/k as the height of the tree goes to infinity. We show that when k>2D/ln(D), with high probability, conditioned on a random coloring of the leaves, the bias at the root decays exponentially in the height of the tree. This is joint work with Juan Vera and Eric Vigoda.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.