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Integrable probability: from representation theory to MacDonald processes. (English) Zbl 1295.82023

Summary: 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.

MSC:

82C22 Interacting particle systems in time-dependent statistical mechanics
60J65 Brownian motion
82D60 Statistical mechanics of polymers
05B45 Combinatorial aspects of tessellation and tiling problems
82-02 Research exposition (monographs, survey articles) pertaining to statistical mechanics
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