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arXiv · 2103.00669

Route Lengths in Invariant Spatial Tree Networks

David J. Aldous
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Abstract

Is there a constant $r_0$ 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 $r > r_0$? 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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David J. Aldous. 2021-03-01. Route Lengths in Invariant Spatial Tree Networks. https://arxiv.org/abs/2103.00669

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