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Consider the problem of approximately counting weighted independent sets of a graph G with activity &#955;, i.e., where the weight of an independent set I is &#955;<sup>|I|</sup>. We present a novel analysis yielding a deterministic approximation scheme which runs in polynomial time for <i>any</i> graph of maximum degree &#916; and &#955;&lt;(More)
The paper considers spin systems on the d-dimensional integer lattice Z d with nearest-neighbor interactions. A sharp equivalence is proved between decay with distance of spin correlations (a spatial property of the equilibrium state) and rapid mixing of the Glauber dynamics (a temporal property of a Markov chain Monte Carlo algorithm). Specifically, we(More)
Consider k-colorings of the complete tree of depth ℓ and branching factor ∆. If we fix the coloring of the leaves, for what range of k is the root uniformly distributed over all k colors (in the limit ℓ → ∞)? This corresponds to the threshold for uniqueness of the infinite-volume Gibbs measure. It is straightforward to show the existence of colorings of the(More)
We study the mixing time of the Glauber dynamics for general spin systems on bounded-degree trees, including the Ising model, the hard-core model (independent sets) and the antiferromagnetic Potts model at zero temperature (colorings). We generalize a framework, developed in our recent paper [18] in the context of the Ising model, for establishing mixing(More)
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