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Let a i , b i , i = 0, 1, 2,. .. be drawn uniformly and independently from the unit interval, and let t be a fixed real number. Let a site (i, j) ∈ N 2 be open if a i + b j ≤ t, and closed otherwise. We obtain a simple, exact expression for the probability Θ(t) that there is an infinite path (oriented or not) of open sites, containing the origin. Θ(t) is… (More)

In coordinate percolation on an positive orthant of the n-dimensional lattice Z n with a given threshold value, 1 + t, random variables a i (k) are uniform on [0, 1] to each pair of integers (i, k) with 1 ≤ i ≤ n and k ≥ 0. A point v = (v 1 ,. .. , v n) is open if a 1 (v 1) + a 2 (v 2) + · · · + a n (v n) < 1 + t and closed otherwise. What is the… (More)

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