School Seminars and Colloquia

Domino Tilings of an Aztec Diamond

Statistical Mechanics/Combinatorics Seminar

by Eric Nordenstam


Institution: Department of Mathematics, KTH, Stockholm, Sweden
Date: Mon 17th March 2008
Time: 1:00 PM
Location: Room 213, Richard Berry Building, The University of Melb

Abstract: There has been a lot of work in recent years about tilings of
various planar regions with different sorts of tiles, for example dominoes
or rhombuses. I shall talk about tilings with dominoes of so called Aztec
diamonds. The shuffling algorithm (introduced by Elkies et al) for
sampling a tiling uniformly at random can be seen as a certain dynamics
on a set of interacting particles. This is a discretization of a model
of interlacing Brownian motions recently studied by Warren. As an
application of these results, I will sketch a new proof of the fact
that, in a sutable scaling limit of large Aztec diamonds, one can
recover the distribution of the eigenvalues of a GUE matrix and its
principal minors.

For More Information: Iwan Jensen I.Jensen@ms.unimelb.edu.au