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Delocalisation of the two-dimensional Lipschitz model
- Speaker(s)
- Piotr Miłoś
- Affiliation
- Uniwersytet Warszawski
- Date
- April 11, 2013, 12:15 p.m.
- Room
- room 3260
- Seminar
- Seminar of Probability Group
We consider a random two-dimensional surface satisfying a Lipschitz constraint. The surface is uniformly chosen from the set of all real-valued Lipschitz functions on a two-dimensional discrete torus. Our main result is that the surface delocalizes, having fluctuations whose variance is at least logarithmic in the size of the torus. The result answers an open question mentioned by Brascamp, Lieb and Lebowitz.
In the talk I will also outline the proof method which follows closely the approach of Richthammer, who developed a variant of the Mermin-Wagner method applicable to hard-core constraints.
I will further address potential extensions and open questions concerning tother surface models.
This is a joint work with R. Peled (U of Tel Aviv).
