Mathematics – Probability
Scientific paper
2012-02-17
Mathematics
Probability
AMSLaTeX, 47 pages, 20 figures
Scientific paper
A Gelfand-Tsetlin scheme of depth N is a triangular array with m integers at level m, m=1,...,N, subject to certain interlacing constraints. We study the ensemble of uniformly random Gelfand-Tsetlin schemes with arbitrary fixed N-th row. We obtain an explicit double contour integral expression for the determinantal correlation kernel of this ensemble (and also of its q-deformation). This provides new tools for asymptotic analysis of uniformly random lozenge tilings of polygons on the triangular lattice; or, equivalently, of random stepped surfaces. We work with a class of polygons which allows arbitrarily large number of sides. We show that the local limit behavior of random tilings (as all dimensions of the polygon grow) is directed by ergodic translation invariant Gibbs measures. The slopes of these measures coincide with the ones of tangent planes to the corresponding limit shapes described by Kenyon and Okounkov in arXiv:math-ph/0507007. We also prove that at the edge of the limit shape, the asymptotic behavior of random tilings is given by the Airy process. In particular, our results cover the most investigated case of random boxed plane partitions (when the polygon is a hexagon).
No associations
LandOfFree
Asymptotics of Random Lozenge Tilings via Gelfand-Tsetlin Schemes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Asymptotics of Random Lozenge Tilings via Gelfand-Tsetlin Schemes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Asymptotics of Random Lozenge Tilings via Gelfand-Tsetlin Schemes will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-35990