Anita Kollwitz

Franco Severo, ETH Zürich: Existence of phase transition for percolation using the GFF (Oberseminar Mathematische Stochastik)

Wednesday, 10.01.2024 14:00 im Raum SRZ 216

Mathematik und Informatik

We consider the classical Bernoulli percolation model on an infinite connected graph G. One of the most fundamental questions in the field is to understand for which graphs G the critical point for the emergence of an infinite connected component is non-trivial, i.e. $p_c(G)\in(0,1)$. While it is easy to prove that $p_c>0$ under very mild conditions, proving $p_c<1$ is a much harder problem. In fact, it is also easy to see that $p_c=1$ if $G$ has linear volume growth. In their seminal paper from 1996, Benjamini and Schramm conjectured that the converse is true for transitive graphs, i.e. $p_c(G)<1$ for every transitive graph G with superlinear volume growth. In this talk, we report on works proving this conjecture as well as a uniform upper bound for the case of Cayley graphs. The proofs rely on an interpolation scheme used to compare Bernoulli percolation with the excursion sets of the Gaussian Free Field, a strongly correlated percolation model for which one can easily prove the existence of a supercritical phase. Based on joint works with H. Duminil-Copin, S. Goswami, A. Raoufi, A. Yadin and C. Panagiotis.

Angelegt am Thursday, 26.10.2023 12:01 von Anita Kollwitz
Geändert am Monday, 08.01.2024 09:27 von Anita Kollwitz
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