A lower bound for the chemical distance in sparse long-range percolation models
نویسنده
چکیده
We consider long-range percolation in dimension d ≥ 1, where distinct sites x and y are connected with probability px,y ∈ [0, 1]. Assuming that px,y is translation invariant and that px,y = ‖x−y‖ −s+o(1) with s > 2d, we show that the graph distance is at least linear with the Euclidean distance.
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تاریخ انتشار 2008