Seminars & Colloquia Calendar

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Special Colloquium

Gibbs measures, arctic curves, and random interfaces

Leonid Petrov, University of Virginia

Location:  Hill 705
Date & time: Monday, 03 December 2018 at 3:30PM - 4:50PM

Abstract:  I will discuss random lattice configurations in two dimensions whose probability distribution follows some version of a Gibbs property. Examples include random (lozenge or domino) tilings and square ice (six vertex) model. Gibbs measures with fixed boundary conditions often display arctic curve phenomena, i.e., a coexistence of different phases. I will outline several results on the local behavior of random configurations in the bulk of a phase or at an interface between phases, and on global asymptotics leading to the Gaussian Free Field. I will also describe certain new Markov dynamics preserving the class of Gibbs measures which adds an extra dimension to the picture.

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