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We consider the problem of sampling independent sets of a graph with maximum degree. The weight of each independent set is expressed in terms of a xed positive parameter 2 ?2 , where the weight of an independent set is jj. The Glauber dynamics is a simple Markov chain Monte Carlo method for sampling from this distribution. We show fast convergence of this(More)
We study a simple Markov chain, known as the Glauber dynamics , for randomly sampling (proper) k-colorings of an input graph G on n vertices with maximum degree ∆ and girth g. We prove the Glauber dynamics is close to the uniform distribution after O(n log n) steps whenever k > (1 +)∆, for all > 0, assuming g ≥ 11 and ∆ = Ω(log n). The best previously known(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)
We present an improved coupling technique for analyzing the mixing time of Markov chains. Using our technique, we simplify and extend previous results for sampling colorings and independent sets. Our approach uses properties of the stationary distribution to avoid worst-case configurations which arise in the traditional approach.As an application, we show(More)
We study two widely used algorithms, Glauber dynamics and the Swendsen-Wang algorithm, on rectangular subsets of the hypercubic lattice Z d. We prove that under certain circumstances, the mixing time in a box of side length L with periodic boundary conditions can be exponential in L d−1. In other words, under these circumstances, the mixing in these widely(More)
We study a simple Markov chain, known as the Glauber dynamics, for generating a random k-coloring of a n-vertex graph with maximum degree /spl Delta/. We prove that the dynamics converges to a random coloring after O(n log n) steps assuming k /spl ges/ k/sub 0/ for some absolute constant k/sub 0/, and either: (i) k//spl Delta/ > /spl alpha/* /spl ap/ 1.763(More)