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Research seminar in Discrete Mathematics
Research seminar in Discrete Mathematics
Supercritical sharpness of percolation
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
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 $p > p_c$.