## Mèliot, Pierre-Loïc - Fluctuations of central measures on partitions

dmtcs:3048 - Discrete Mathematics & Theoretical Computer Science, January 1, 2012, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Fluctuations of central measures on partitions

Authors: Mèliot, Pierre-Loïc

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.

Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Section: Proceedings
Published on: January 1, 2012
Submitted on: January 31, 2017
Keywords: Random partitions, generalized riffle shuffles, representation theory of the infinite symmetric group.,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]