Fluctuations of particle systems determined by Schur generating functions

Abstract

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.

65 pages, 4 figures. v3: some misprints corrected compared to the journal version

References in corpus (3)

• Second Order Freeness and Fluctuations of Random Matrices: II. Unitary Random Matrices
• Kerov's central limit theorem for Schur-Weyl measures of parameter 1/2
• An asymptotic log-Fourier interpretation of the R-transform

Cited by in corpus (19)

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• Matrix addition and the Dunkl transform at high temperature
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• Height Fluctuations of Random Lozenge Tilings Through Nonintersecting Random Walks
• Lozenge tilings and the Gaussian free field on a cylinder
• Airy Point Process via Supersymmetric Lifts
• Bipartite dimer model: perfect t-embeddings and Lorentz-minimal surfaces
• Macdonald cumulants, $G$-inversion polynomials and $G$-parking functions
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• Fluctuations in the Aztec diamonds via a space-like maximal surface in Minkowski 3-space
• A Quantized Analogue of the Markov-Krein Correspondence
• $\beta$-Nonintersecting Poisson Random Walks: Law of Large Numbers and Central Limit Theorems
• How to Draw a Correlation Function
• Asymptotics of Schur functions on almost staircase partitions
• A power series identity and Bessel-type integrals over unitary groups