Dear Colleagues,

We would like to invite you to the following seminar that will take place on July 15 at 14.30. The seminar will be held in person and online via the Zoom platform.

The organizers,

Alessandra Bianchi, Giorgia Callegaro, Marco Formentin _____________________________________________________

Speaker: Maximilian Nitzschner (NYU Courant Institute)

Title: Phase transition for level-set percolation of the membrane model

Date and time: Friday, JULY 15 - 14.30

Place: room 2BC30 at the Department of Mathematics, University of Padova

Zoom link: https://unipd.zoom.us/j/85663140963 (meeting ID 856 6314 0963), available also on the webpage https://www.math.unipd.it/~bianchi/seminari/

Abstract: We consider level-set percolation for the Gaussian membrane model on the integer lattice in dimensions five and higher, and establish that as h varies, a non-trivial percolation phase transition for the level-set above level h occurs at some finite critical level, which is positive in high dimensions. Moreover, we demonstrate the existence of a strongly subcritical phase, in which we provide bounds for the connectivity function of the level-set above h, and a strongly supercritical phase, in which we characterize the geometry of the level-set above level h. As a pivotal tool, we present novel (conditional) decoupling inequalities for the membrane model, which are instrumental in the study of both the subcritical and supercritical phases of its level-sets. This talk is based on joint work with Alberto Chiarini.