Poisson-Voronoi percolation in high dimensions.

Resumen:  

We consider a Poisson point process with constant intensity in $ \mathbb{R}^d $ and independently color each cell of the resulting random Voronoi tessellation black with probability $ p $. The critical probability $ p_c(d) $ is the value for $ p $ above which there exists
almost surely an unbounded black component and almost surely does not for values below. In this talk I aim to give an overview of the model and sketch some ideas of a proof that $ p_c(d)=(1+o(1)) e d^{-1} 2^{-d} $, as $ d\to\infty $. We also obtain the corresponding result for site percolation on the Poisson-Gabriel graph, where $ p_c(d)=(1+o(1))2^{-d} $.

Posted on Apr 1, 2026 in Seminario de Probabilidades de Chile, Seminars