Angelo Abächerli (ETH Zürich): Level-set percolation of the Gaussian free field on large d-regular expanders

In this joint project with Jiří Černý we study level-set percolation of the zero-average Gaussian free field on a class of large d-regular graphs with d larger equal 3, containing d-regular expanders of large girth and typical realisations of random d-regular graphs. Through suitable local approximations of the zero-average Gaussian free field by the Gaussian free field on the infinite d-regular tree we are able to establish a phase transition for level-set percolation of the zero-average Gaussian free field which occurs at the critical value for level-set percolation in the infinite model.