Electronic Journal of Probability
- Electron. J. Probab.
- Volume 19 (2014), paper no. 15, 41 pp.
Scale-invariant random spatial networks
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.
Electron. J. Probab., Volume 19 (2014), paper no. 15, 41 pp.
Accepted: 28 January 2014
First available in Project Euclid: 4 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 90B20: Traffic problems
This work is licensed under a Creative Commons Attribution 3.0 License.
Aldous, David. Scale-invariant random spatial networks. Electron. J. Probab. 19 (2014), paper no. 15, 41 pp. doi:10.1214/EJP.v19-2920. https://projecteuclid.org/euclid.ejp/1465065657