| Uniqueness of Uniform Random Colorings of Regular Trees (2001) | |||||||||||||||
Abstract | |||||||||||||||
| A q-coloring of an in nite graph G is a homomorphism from G to the complete graph K q on q vertices. A probability measure on the set of q- colorings of G is said to be a Gibbs measure for q-colorings of G for uniform activities if for every nite portion U of G and almost every q-coloring of G n U , the conditional distribution on the coloring of U given the coloring of GnU is uniform (on the set of colorings that are admissable when the coloring of the boundary of U is taken into account). | |||||||||||||||
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