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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Delocalization of two-dimensional random surfaces with hard-core constraints

## Delocalization of two-dimensional random surfaces with hard-core constraintsAdd to your list(s) Download to your calendar using vCal - Peled, R (Tel Aviv University)
- Tuesday 17 March 2015, 11:30-12:30
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact Mustapha Amrani. Random Geometry Co-author: Piotr Milos (University of Warsaw) 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. We rely also on the reflection positivity of the random surface model. The result answers a question mentioned by Brascamp, Lieb and Lebowitz on the hammock potential and a quest ion of Velenik. All terms will be explained in the talk. Joint work with Piotr Milos. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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