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What trips me up is that typically one thinks of Poisson in terms of the whole $\mathbb R^3$ and the intensity, whereas complexity requires the thinking to shift to $n$ iid points in a bounded set (I think?). To be honest, I am struggling to even understand the question correctly.
@alesia: I suppose what I'm asking about is a stronger result? Either would be interesting, though. I've edited the question a little. 27 is roughly the number of vertices of a Voronoi cells, which would correspond to neighboring tetrahedra, I think degree of a Delaunay vertex corresponds to the number of edges, which is around 40.6 (pg. 316 in Okabe et al. ). Are you suggesting we bound the probability using Chebyshev's inequality to prove the asymptotic result?
