Chilean Probability Seminar: Supercritical Sharpness of Percolation

Abstract:

Given an infinite transitive graph (such as the standard lattice Z^d), build a random subgraph by independently including each edge with probability p. This model undergoes a phase transition as p varies across the critical value p_c marking the emergence of an infinite component. A fundamental result is that for any fixed p<p_c, the probability that a given vertex is in a component of size at least n decays exponentially with n. We will prove the analogous result for the supercritical regime, p>p_c. Based on a joint work with Easo, Ramanan-Radhakrishnan, Sudakov, and Tassion.

Venue: Maryam Mirzakhani Room, North Tower, 6th Floor, Beauchef 851.

Hybrid-format event.

The link to join the seminar is Zoom meeting:

ID de reunión: 845 2183 4914
Código de acceso: 997973
Código de acceso: 997973