Anchored expansion, speed and the Poisson-Voronoi tessellation in symmetric spaces

DOI10.1214/17-AOP1216zbMath1430.60019arXiv1409.4312OpenAlexW2808453398WikidataQ129686784 ScholiaQ129686784MaRDI QIDQ1660623

Itai Benjamini, Elliot Paquette, Joshua Pfeffer

Publication date: 16 August 2018

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.4312

zbMATH Keywords

tessellationexpansionisoperimetric constanthyperbolic spacehyperbolic geometryPoisson processVoronoi tilingunimodular random graphanchored isoperimetric constant

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Tilings in (2) dimensions (aspects of discrete geometry) (52C20)

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Indistinguishability of trees in uniform spanning forests ⋮ On the speed of distance stationary sequences ⋮ Beta-star polytopes and hyperbolic stochastic geometry ⋮ The critical probability for Voronoi percolation in the hyperbolic plane tends to 1/2 ⋮ Intersections of Poisson \(k\)-flats in constant curvature spaces ⋮ Sparse expanders have negative curvature ⋮ Coalescing random walk on unimodular graphs ⋮ Supercritical causal maps: geodesics and simple random walk ⋮ Supercritical percolation on nonamenable graphs: isoperimetry, analyticity, and exponential decay of the cluster size distribution ⋮ Unimodular hyperbolic triangulations: circle packing and random walk ⋮ Planar stochastic hyperbolic triangulations ⋮ Anchored expansion of Delaunay complexes in real hyperbolic space and stationary point processes ⋮ Distributional lattices on Riemannian symmetric spaces ⋮ Hyperbolic and parabolic unimodular random maps

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