Daniel de la Riva (University of Bath)
will speak on
Continuity of the phase transition for long-range Bernoulli percolation with exponential decay on $\mathbb{Z}^{2}$
Time: 2:00PM
Date: Wed 28th October 2026
Location: N0.20 - Science North
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Abstract: We prove continuity of the phase transition for long-range Bernoulli percolation on $\mathbb{Z}^{2}$ with connection probabilities that decay at least exponentially fast. This extends earlier work by Duminil-Copin, Sidoravicius, and Tassion on slabs. Our proof establishes a finite-size criterion that allows us to run a renormalisation argument. As a corollary, we obtain supercritical sharpness, in the sense that for every $\beta>\beta_c$, there exists a unique macroscopic cluster in large boxes with high probability.
(This talk is part of the Probability series.)
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