Simplicial percolation

Abstract: This talk introduces weak and strong simplicial percolation as models for continuum percolation based on random simplicial complexes in Euclidean space. Weak simplicial percolation is defined through infinite sequences of k-simplices sharing a (k-1)-dimensional face. In contrast, strong simplicial demands the existence of an infinite k-surface, thereby generalizing the lattice notion of plaquette percolation. We discuss the sharp phase transition for weak simplicial percolation and derive several relationships between weak simplicial percolation, strong simplicial percolation, and classical vacant continuum percolation. We will also draw connections to a variety of topological models for percolation that have been proposed recently in the literature. This talk is based on joint work with Daniel Valesin.

computational geometryalgebraic topologycombinatoricsgeometric topologyprobability

Audience: advanced learners

Asia Pacific Seminar on Applied Topology and Geometry