Zusammenfassung für den Vortrag am 16.01.2015 (10:00 Uhr)
Arbeitsgemeinschaft ANGEWANDTE ANALYSISPierre-Francois Rodriguez (ETH Zurich, Department of Mathematics)
On level-set percolation for the Gaussian free field in high dimensions
We investigate the percolation model obtained by considering level sets of the Gaussian free field on the d-dimensional lattice above a given height h. It has recently been proved that, as h varies, this model exhibits a non-trivial percolation phase transition in all dimensions d greater or equal to 3. We show that the associated critical density behaves like 1/dˆ1 + o(1) as d goes to infinity. The proof gives the (principal) asymptotics of the corresponding critical height h˙*(d). Moreover, it shows that a related parameter h˙**(d), which characterizes a strongly subcritical regime, is in fact asymptotically equivalent to h˙*(d).