Fluctuations of random surfaces

Speaker(s): 
Ron Peled (Tel Aviv University)
Date: 
Wednesday, April 27, 2016 - 6:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

We study the fluctuations of random surfaces on a two-dimensional discrete torus. The random surfaces we consider are defined via a nearest-neighbor pair potential which we require to be twice continuously differentiable on a (possibly infinite) interval and infinity outside of this interval. This includes the case of the so-called hammock potential, when the random surface is uniformly chosen from the set of all surfaces satisfying a Lipschitz constraint. Our main result is that these surfaces delocalize, having fluctuations whose variance is at least of order log n, where n is the side length of the torus. The main tool in our analysis is an adaptation to the lattice setting of an algorithm of Richthammer, who developed a variant of a Mermin-Wagner-type argument applicable to hard-core constraints. The result answers a question mentioned by Brascamp, Lieb and Lebowitz on the hammock potential and a question of Velenik. All terms will be explained in the talk. Joint work with Piotr Milos.