Delocalization of two-dimensional random surfaces with hard-core constraints
59 mins 23 secs,
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About this item
| Description: |
Peled, R (Tel Aviv University)
Tuesday 17 March 2015, 11:30-12:30 |
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| Created: | 2015-03-18 13:00 |
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| Collection: | Random Geometry |
| Publisher: | Isaac Newton Institute |
| Copyright: | Peled, R |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | 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. |
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