Percolation on Hyperbolic Poisson-Voronoi Tessellations

Explore percolation on hyperbolic Poisson-Voronoi tessellations in this 32-minute lecture by Tobias Mueller from the Hausdorff Center for Mathematics. Delve into the concept of coloring cells in a hyperbolic Poisson-Voronoi tessellation and the conditions for percolation occurrence. Examine joint work with doctoral candidate Ben Hansen that addresses a conjecture and open question posed by Benjamini and Schramm about the critical probability for percolation. Investigate the unique dependence of the critical value on the intensity of the Poisson process in hyperbolic space, contrasting with Euclidean Poisson-Voronoi percolation. Cover topics including Poisson-Voronoi tessellations, hyperbolic plane representation, coordinate maps, Poisson disk, percolation models, and intuition behind lower bounds.

Introduction
PoissonVoronoi tessellations
Small domain results
Definition of hyperbolic plane
Representation of hyperbolic plane
Coordinate maps
Poisson disk
Percolation model
Audetrom et al
Percolation diagram
Percolation conjecture
First result
Intuition
Lower bound
Conclusion