Integrable probability: From representation theory to Macdonald processes

2013/10/30

(with Alexei Borodin)
Probability Surveys, 11 (2014), 1-58arXiv:1310.8007 [math-ph]

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.

Large scale and long time behavior of a jumping interacting particle system
Large scale and long time behavior of a jumping interacting particle system