Zusammenfassung für den Vortrag am 30.01.2018 (15:15 Uhr)Oberseminar ANALYSIS - PROBABILITY
Alexander Drewitz (Universität zu Köln)
Sign clusters of the Gaussian free ﬁeld percolate on ℤd, d ≥ 3
We consider level set percolation for the Gaussian free field on the Euclidean lattice in dimensions larger than or equal to three. It had previously been shown by Bricmont, Lebowitz, and Maes that the critical level is non-negative in any dimension and finite in dimension three. Rodriguez and Sznitman have extended this result by proving that it is finite for all dimensions, and positive for all large enough dimensions. We show that the critical parameter is positive in any dimension larger than or equal to three. In particular, this entails the percolation of sign clusters of the Gaussian free field. This talk is based on joint work with A. Prévost (Köln) and P.-F. Rodriguez (Los Angeles).