Ron Peled


Tel Aviv University

On the site percolation threshold of circle packings and planar graphs, with application to the loop O(n) model

A circle packing is a collection of disks in the plane with disjoint interiors. We show that there exists p>0 such that the following holds for any circle packing with at most countably many accumulation points: When coloring each circle red with probability p, independently, there is no infinite connected component of red circles, almost surely. This implies, in particular, that the site percolation threshold of any planar recurrent graph is at least p. The result partially answers a question of Benjamini. Time permitting, we will discuss an application, joint with Nick Crawford, Alexandar Glazman and Matan Harel, to the existence of macroscopic loops in the loop O(n) model on the hexagonal lattice.

Date: Tue 16 Apr 2019

Start Time: 11:30

End Time: 12:30

861 | Electrical Eng. Building