Chemical distances and the incipient infinite cluster in percolation

by Prof. Jack Hanson (Universität Hamburg)

Tuesday 2 Dec 2025, 17:00 → 18:00 Europe/Berlin

H4 (Geomatikum)

 Physicists have been interested in percolation since at least the 1970s as a model for transport properties of disordered media. This has led to tantalizing conjectures about the model -- for instance, the behavior of random walk on percolation clusters -- which require us to understand aspects of its large-scale geometry. We will discuss several of these, particularly focusing on the behavior of the chemical (graph) distance and especially in the high-dimensional setting. Here a recent preprint of the speaker finds the exact limiting distribution of the chemical distance between two distant vertices, conditional on them lying in the same percolation cluster.