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2014 Scale-invariant random spatial networks
David Aldous
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Electron. J. Probab. 19: 1-41 (2014). DOI: 10.1214/EJP.v19-2920


Real-world road networks have an approximate scale-invariance property; can one devise mathematical models of random networks whose distributions are exactly invariant under Euclidean scaling? This requires working in the continuum plane. We introduce an axiomatization of a class of processes we call "scale-invariant random spatial networks", whose primitives are routes between each pair of points in the plane. We prove that one concrete model, based on minimum-time routes in a binary hierarchy of roads with different speed limits, satisfies the axioms, and note informally that two other constructions (based on Poisson line processes and on dynamic proximity graphs) are expected also to satisfy the axioms. We initiate study of structure theory and summary statistics for general processes in this class.


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David Aldous. "Scale-invariant random spatial networks." Electron. J. Probab. 19 1 - 41, 2014.


Accepted: 28 January 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1305.90104
MathSciNet: MR3164768
Digital Object Identifier: 10.1214/EJP.v19-2920

Primary: 60D05
Secondary: 90B20

Keywords: Poisson process , scale invariance , spatial network


Vol.19 • 2014
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