Supercritical sharpness of percolation
Organizers
Jie Ma
, Benjamin Sudakov
Speaker
Philip Easo
Time
Tuesday, March 24, 2026 5:05 PM - 6:15 PM
Venue
Online
Online
Zoom 787 662 9899
(BIMSA)
Abstract
Abstract: Given an infinite transitive graph (such as the lattice Z^d), consider the random subgraph obtained by independently retaining each edge with probability p. This model undergoes a phase transition as p varies across a critical value p_c that marks the emergence of an infinite component. A classical result states that for each p < p_c, the probability that a given vertex belongs to a component of size at least n decays exponentially in n. Sahar Diskin, Ritvik Ramanan Radhakrishnan, Benny Sudakov, Vincent Tassion, and I have recently proved the analogous result for p > p_c.