For more information about this meeting, contact John Roe, Dmitri Burago.
|Title:||Random 3D surfaces and tehir asymptotic behavior|
|Seminar:||Geometry Luncheon Seminar|
|Speaker:||Leonid Petrov, Northeastern University|
|I will discuss the model of uniformly random tilings of polygons drawn on the regular triangular lattice by lozenges of three types (equivalent formulations: dimer models on the honeycomb lattice, or random 3D stepped surfaces glued out of 1x1x1 boxes). Asymptotic questions about these tilings have received a significant attention over the past years. Kenyon, Okounkov, and their co-authors (1998-2007) proved the law of large numbers: when the polygon is fixed and the mesh of the lattice goes to zero, the random surface concentrates around a deterministic limit shape which is algebraic in a certain sense. Via an explicit understanding of the correlations in the model, I managed to obtain finer asymptotics of random surfaces. I will discuss the local geometry of the surfaces, behavior of interfaces between phases (which manifests the Kardar-Parisi-Zhang universality), and global fluctuations of random surfaces (described by the Gaussian Free Field).|
Room Reservation Information
|Date:||11 / 08 / 2013|
|Time:||12:00pm - 01:30pm|