As Poisson intensity tends to infinity, the point process of suitably transformed longest edges in empty region graphs converges to a Poisson process on R^d x R x L^d, and the max length converges to Gumbel.
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Limit laws for longest edges in empty region graphs
As Poisson intensity tends to infinity, the point process of suitably transformed longest edges in empty region graphs converges to a Poisson process on R^d x R x L^d, and the max length converges to Gumbel.