Affiliation:
1. Department of Mathematics Weizmann Institute of Science Rehovot Israel
2. Courant Institute New York University New York New York USA
Abstract
AbstractWe study the distribution of the maximum of a large class of Gaussian fields indexed by a box and possessing logarithmic correlations up to local defects that are sufficiently rare. Under appropriate assumptions that generalize those in Ding et al., we show that asymptotically, the centered maximum of the field has a randomly‐shifted Gumbel distribution. We prove that the two dimensional Gaussian free field on a super‐critical bond percolation cluster with p close enough to 1, as well as the Gaussian free field in i.i.d. bounded conductances, fall under the assumptions of our general theorem.
Funder
European Research Council
Israel Science Foundation
Subject
Applied Mathematics,General Mathematics
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