Integrable probability: From representation theory to Macdonald processes
arXiv:1310.8007
Abstract
These are lecture notes for a mini-course given at the Cornell Probability Summer School in July 2013. Topics include lozenge tilings of polygons and their representation theoretic interpretation, the (q,t)-deformation of those leading to the Macdonald processes, nearest neighbor dynamics on Macdonald processes, their limit to semi-discrete Brownian polymers, and large time asymptotic analysis of polymer's partition function.
49 pages; 22 figures; v3, v4: minor typos fixed