ANCHORED EXPANSION, SPEED AND THE POISSON-VORONOI TESSELLATION IN SYMMETRIC SPACES

• 成果类型: Article
• 署名作者: Benjamini, Itai; Paquette, Elliot; Pfeffer, Joshua
• 署名单位: Weizmann Institute of Science; University System of Ohio; Ohio State University; Massachusetts Institute of Technology (MIT)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1216
• 发表日期: 2018
• 页码: 1917-1956
• 关键词: random-walk; hyperbolic plane; circle packings; graphs; percolation; triangulations; realizability; MANIFOLDS

摘要

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.