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[en] We consider oriented long-range percolation on a graph with vertex set and directed edges of the form , for x, y in and . Any edge of this form is open with probability , independently for all edges. Under the assumption that the values do not vanish at infinity, we show that there is percolation even if all edges of length more than k are deleted, for k large enough. We also state the analogous result for a long-range contact process on .
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