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2021 Route lengths in invariant spatial tree networks
David Aldous
Author Affiliations +
Electron. Commun. Probab. 26: 1-12 (2021). DOI: 10.1214/21-ECP401

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.

Acknowledgments

I thank Yuval Peres and Russ Lyons for the references to [10, 15], and Geoffrey Grimmett for comments on the contour method and for catching an error in an early draft. I also thank an anonymous referee for prompting some more detailed proofs.

Citation

Download Citation

David Aldous. "Route lengths in invariant spatial tree networks." Electron. Commun. Probab. 26 1 - 12, 2021. https://doi.org/10.1214/21-ECP401

Information

Received: 2 March 2021; Accepted: 9 May 2021; Published: 2021
First available in Project Euclid: 2 June 2021

Digital Object Identifier: 10.1214/21-ECP401

Subjects:
Primary: 60D05, 60K35

JOURNAL ARTICLE
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