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SUMMARY:Maximilian Nitzscher (NYU Courant)
DTSTART:20220211T173000Z
DTEND:20220211T183000Z
DTSTAMP:20260423T005722Z
UID:PatC/55
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PatC/55/">Ph
 ase transition for level-set percolation of the membrane model</a>\nby Max
 imilian Nitzscher (NYU Courant) as part of Probability and the City Semina
 r\n\n\nAbstract\nWe consider level-set percolation for the Gaussian membra
 ne model on the integer lattice in dimensions five and higher\, and establ
 ish that as h varies\, a non-trivial percolation phase transition for the 
 level-set above level h occurs at some finite critical level\, which we sh
 ow to be positive in high dimensions. Moreover\, we demonstrate the existe
 nce of a strongly subcritical phase\, in which we provide bounds for the c
 onnectivity function of the level-set above h\, and a strongly supercritic
 al phase\, in which we characterize the geometry of the level-set above le
 vel h. As a main tool\, we present novel decoupling inequalities for the m
 embrane model\, which are instrumental in the study of both the subcritica
 l and supercritical phases of its level-sets. This talk is based on joint 
 work with Alberto Chiarini.\n
LOCATION:https://researchseminars.org/talk/PatC/55/
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