Integrable probability: From representation theory to Macdonald processes

30 Apr 2017  ·  Borodin Alexei, Petrov Leonid ·

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.

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Probability Statistical Mechanics Mathematical Physics Combinatorics Mathematical Physics Representation Theory
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