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Discrete Mathematics & Theoretical Computer Science |
We study the fluctuations of models of random partitions $(\mathbb{P}_n,ω )_n ∈\mathbb{N}$ stemming from the representation theory of the infinite symmetric group. Using the theory of polynomial functions on Young diagrams, we establish a central limit theorem for the values of the irreducible characters $χ ^λ$ of the symmetric groups, with $λ$ taken randomly according to the laws $\mathbb{P}_n,ω$ . This implies a central limit theorem for the rows and columns of the random partitions, and these ``geometric'' fluctuations of our models can be recovered by relating central measures on partitions, generalized riffle shuffles, and Brownian motions conditioned to stay in a Weyl chamber.
Source : ScholeXplorer
IsRelatedTo ARXIV 1303.4313 Source : ScholeXplorer IsRelatedTo DOI 10.1007/s10801-013-0480-7 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1303.4313
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