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Research Bernoulli Institute Calendar

Seminar Algebra - Prof. dr. T. Müller University of Groningen

When:Th 25-02-2021 17:00 - 18:00
Where:Online (see below)

Title: Percolation on hyperbolic Poisson-Voronoi tessellations


I will discuss percolation on the Voronoi tessellation generated by a homogeneous Poisson point process on the hyperbolic plane. That is, we colour each cell of the hyperbolic Poisson-Voronoitessellation black with probability and white with probability 1−p, independently of the colours of all other cells. We say that percolation occurs if there is an infinite connected cluster of black cells. I will sketch joint work with the doctoral candidate Ben Hansen that resolves a conjecture and an open question, posed by Benjamini and Schramm about twenty years ago, on the behaviour of the“critical probability for percolation” as a function of the intensity parameter of the underlying Poisson process. (Unlike in Euclidean Poisson-Voronoi percolation, this critical value depends on the intensity of the Poisson process.) Based on joint work with Benjamin Hansen.