11/12/2015 - 16:30

11/12/2015 - 17:30

Speaker:

Phil Sosoe (Harvard University)

Location:

Burnside Hall, Rm. 920 (McGill University)

Abstract:

The chemical distance is the graph distance inside percolation clusters. In the supercritical phase, this distance is known to be linear with exponential probability, enabling a detailed study of processes like random walks on the infinite cluster. By contrast, at the critical point, the distance is known to be longer than Euclidean by some (unknown) power. I will discuss this and some bounds on distance, as well as a result comparing the chemical distance to the size of the lowest crossing. Joint work with Jack Hanson and Michael Damron.