Fluctuations of particle systems determined by Schur generating functions
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 certa...
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier BV,
2020-03-27T17:36:32Z.
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| Online Access: | Get fulltext |
| Summary: | 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 National Science Foundation (U.S.) (Grant DMS-1407562) |
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