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Anchored expansion in the hyperbolic Poisson Voronoi tessellation

By Elliot Paquette

Also appears in collection : Spectrum of random graphs / Spectre de graphes aléatoires

We show that 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 speed. We include a section of open problems and conjectures on the topics of stationary geometric random graphs and the hyperbolic Poisson Voronoi tessellation.

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Citation data

  • DOI 10.24350/CIRM.V.18912903
  • Cite this video Paquette, Elliot (07/01/2016). Anchored expansion in the hyperbolic Poisson Voronoi tessellation. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18912903
  • URL https://dx.doi.org/10.24350/CIRM.V.18912903

Bibliography

  • Benjamini, I., Paquette, E., & Pfeffer, J. (2014). Anchored expansion in the hyperbolic Poisson Voronoi tessellation. <arXiv:1409.4312> - http://arxiv.org/abs/1409.4312

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