Delocalization of random Lipschitz functions in two dimensions

Ron Peled előadásának absztraktja

(Joint work with Piotr Miłoś)

2013. augusztus 30. péntek, 15:00

 
 

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. Our technique follows closely the approach of Richthammer, who developed a variant of the Mermin-Wagner method applicable to hard-core constraints. The result answers an open question mentioned by Brascamp, Lieb and Lebowitz on the hammock potential. Extensions and related open problems will also be discussed. Joint work with Piotr Miłoś.


 
Tóth Imre Péter, 2013.08.23