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The random connection model in high dimensions

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By Ronald Meester, Mathew D. Penrose, and Anish Sarkar

Consider a continuum percolation model in which
each pair of points of a $d$-dimensional Poisson process
of intensity $\lambda$ is connected with a probability
which is a function $g$ of the distance between them.
We show that under a mild regularity condition on $g$, the
critical value of $\lambda$, above which an infinite cluster
exists almost surely, is asymptotic, as $d$ goes to infinity,
to the inverse of the integral of $g(|x|)$ over $d$-dimensional space $R^d$.
Statistics and Probability Letters 35, 145-153 (1997).