Random Colorings of a Cayley Tree

  title={Random Colorings of a Cayley Tree},
  author={Graham R. Brightwell},
Probability measures on the space of proper colorings of a Cayley tree (that is, an in nite regular connected graph with no cycles) are of interest not only in combinatorics but also in statistical physics, as states of the antiferromagnetic Potts model at zero temperature, on the \Bethe lattice". We concentrate on a particularly nice class of such measures which remain invariant under parity-preserving automorphisms of the tree. Making use of a correspondence with branching random walks on… CONTINUE READING


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