Fluctuations of particle systems determined by Schur generating functions
Author(s)Bufetov, Alexey; Gorin, Vadim
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We develop a new toolbox for the analysis of the global behavior of stochastic discrete particle systems. We introduce and study the notion of the Schur generating function of a random discrete configuration. Our main result provides a Central Limit Theorem (CLT) for such a configuration given certain conditions on the Schur generating function. As applications of this approach, we prove CLT's for several probabilistic models coming from asymptotic representation theory and statistical physics, including random lozenge and domino tilings, non-intersecting random walks, decompositions of tensor products of representations of unitary groups. Keywords: Schur functions; Asymptotic representation theory; Random tilings
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Advances in Mathematics
Bufetov, Alexey, and Vadim Gorin. “Fluctuations of Particle Systems Determined by Schur Generating Functions.” Advances in Mathematics 338, 7 (November 2018): 702–81.