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Route lengths in invariant spatial tree networks
Abstract
Is there a constant r0 such that, in any invariant tree network linking rate-1 Poisson points in the plane, the mean within-network distance between points at Euclidean distance r is infinite for r > r0? We prove a slightly weaker result. This is a continuum analog of a result of Benjamini et al (2001) on invariant spanning trees of the integer lattice.
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