A U-statistic of a Poisson point process is defined as the sum ∑ f (x₁, · · ·, xk) over all (possibly infinitely many) k-tuples of distinct points of the point process. Using the Malliavin calculus, ...
We consider a version of continuum long-range percolation on finite boxes of ℝd in which the vertex set is given by the points of a Poisson point process and each pair of two vertices at distance r is ...
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