The Annals of Probability
- Ann. Probab.
- Volume 46, Number 4 (2018), 1917-1956.
Anchored expansion, speed and the Poisson–Voronoi tessellation in symmetric spaces
We show that a random walk on a stationary random graph with positive anchored expansion and exponential volume growth has positive speed. We also show that two families of random triangulations of the hyperbolic plane, the hyperbolic Poisson–Voronoi tessellation and the hyperbolic Poisson–Delaunay triangulation, have $1$-skeletons with positive anchored expansion. As a consequence, we show that the simple random walks on these graphs have positive hyperbolic speed. Finally, we include a section of open problems and conjectures on the topics of stationary geometric random graphs and the hyperbolic Poisson–Voronoi tessellation.
Ann. Probab., Volume 46, Number 4 (2018), 1917-1956.
Received: October 2014
Revised: July 2017
First available in Project Euclid: 13 June 2018
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Benjamini, Itai; Paquette, Elliot; Pfeffer, Joshua. Anchored expansion, speed and the Poisson–Voronoi tessellation in symmetric spaces. Ann. Probab. 46 (2018), no. 4, 1917--1956. doi:10.1214/17-AOP1216. https://projecteuclid.org/euclid.aop/1528876818