Abstract:
We illustrate how two percolation models with long-range correlations, vacant set percolation for random interlacements as well as level set percolation for the Gaussian free field, can be understood more profoundly by relating them through the use of isomorphism theorems. As an application, this can be used to show that the critical parameter for level set percolation in ℤd, d ⩾ 3, is positive in any dimension larger than or equal to three, which had been conjectured by Bricmont, Lebowitz and Maes in 1987. If time admits, we will consider applications to other graphs also. This talk is based on joint work with A. Prévost (Köln) and P.-F. Rodriguez (Los Angeles).
Biography:
Alexander Drewitz has been appointed Professor for mathematics at the University of Cologne in 2015. His research focuses on topics in probability theory that find their motivation in statistical mechanics. More precisely, he has been working on problems in random media as well as percolation models with long-range correlations. He has contributed to the investigation of ballisticity for random walk in random environment, the parabolic Anderson model and related trapping models, as well as to the percolation of the Gaussian free field and (the vacant set of) random interlacements.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai