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Random minimal spanning tree and percolation on the *N*-cube

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By Mathew D. Penrose.

The *N*-cube is a graph with 2^{N} vertices
and N2^{N-1} edges.
Suppose independent uniform random edge-weights are assigned,
and let *T* be the spanning tree of minimal (total) weight.
Then the weight of *T* is asymptotic to
(1/*N*)2^{N}
(sum_{i>0}i^{-3})
as *N* tends to infinity.
Asymptotics are also given for the local structure of *T*,
and for the distribution of its *k*-th largest edge-weight,
*k* fixed.
Random Structures and Algorithms 12, 63-82 (1998).