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Supercritical sharpness of percolation

组织者

马杰 , 本杰明·苏达科夫

演讲者

Philip Easo

时间

2026年03月24日 17:05 至 18:15

地点

Online

线上

Zoom 787 662 9899 (BIMSA)

摘要

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 $p > p_c$.