Giant component in the supercritical level-​set percolation of GFF on regular expanders

Vortrag von Prof. Dr. Jiří Černý

Datum: 06.10.21  Zeit: 17.15 - 18.15  Raum: ETH HG G 19.1

In recent works with A. Abächerli, we showed that the level set percolation of the zero-​mean Gaussian free field on a certain class of regular expander graphs exhibits a phase transition. A slight drawback of this result is our description of the supercritical phase where we only could show that the largest connected component is "mesoscopic". In the talk, I will first describe the problem, and then explain how to remove this drawback and how to show that the supercritical level set has an essentially unique giant component.