Bounds for the return probability of the delayed random walk on finite percolation clusters in the critical case
نویسنده
چکیده
By an eigenvalue comparison-technique[16], the expected return probability of the delayed random walk on the finite clusters of critical Bernoulli bond percolation on the two-dimensional Euclidean lattice is estimated. The results are generalised to invariant percolations on unimodular graphs with almost surely finite clusters. A similar method has been used elsewhere[17] to derive bounds for invariant percolation of finite clusters on unimodular transitive graphs. It is adapted here to match the special situation of criticality. The approach followed here involves using the special property of Cartesian Products of finite graphs with cycles of a certain minimal size to be Hamiltonian[1].
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Ja n 20 09 Bounds for the return probability of the delayed random walk on finite percolation clusters in the critical case
By an eigenvalue comparison-technique[20], the expected return probability of the delayed random walk on critical Bernoulli bond percolation clusters on the twodimensional Euclidean lattice is estimated. The results are generalised to invariant percolations on unimodular graphs with almost surely finite clusters. The approach involves using the special property of cartesian products of finite g...
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