【摘 要】
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Let's consider the supercritical Poisson continuous percolation on d-dimensional torus Tdn with volume nd.By adding "long edges " randomly to the largest pe
【机 构】
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School of Math.Sci.,Capital normal Univ.
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Let's consider the supercritical Poisson continuous percolation on d-dimensional torus Tdn with volume nd.By adding "long edges " randomly to the largest percolation cluster,we obtain a random graph Gn.We first prove that the diameter of Gn grows at most polynomially fast in ln n,Secondly,we prove that the random walk on Gn possesses the rapid mixing property,namely,the random walk mixes in time at most polynomially large in ln n.
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