Statistics Seminars: Tropical Combinatorics, Whittaker Functions and Random Polymers.
18 November 2013 14:00 in CM221
Whittaker functions are special functions, which have a central position in representation theory and integrable systems. Surprisingly, they turn out to play a central role in the fluctuation analysis of Random Polymer Models (modelling a random walk in a random potential). In this talk I will explain the emergence of Whittaker functions in the Random Polymer Model, via the use of Tropical Combinatorics, and will describe their role in the computation of the distribution of the corresponding partition function and how this leads to the t^1/3 asymptotic fluctuations and Tracy-Widom distributions. An important role is played by the tropical (or geometric) Robinson-Schensted-Knuth correspodence and its volume preserving properties, which, as a byproduct leads to a new interpretation of Givental's integral formula for Whittaker functions. Based on joint works with I.Corwin, N. O'Connell and T.Sepallainen.
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