Anchored expansion, speed and the Poisson–Voronoi tessellation in symmetric spaces
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. …