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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.