Skip to Main content Skip to Navigation
Conference papers

Kerov's central limit theorem for Schur-Weyl and Gelfand measures (extended abstract)

Abstract : We show that the shapes of integer partitions chosen randomly according to Schur-Weyl measures of parameter $\alpha =1/2$ and Gelfand measures satisfy Kerov's central limit theorem. Thus, there is a gaussian process $\Delta$ such that under Plancherel, Schur-Weyl or Gelfand measures, the deviations $\Delta_n(s)=\lambda _n(\sqrt{n} s)-\sqrt{n} \lambda _{\infty}^{\ast}(s)$ converge in law towards $\Delta (s)$, up to a translation along the $x$-axis in the case of Schur-Weyl measures, and up to a factor $\sqrt{2}$ and a deterministic remainder in the case of Gelfand measures. The proofs of these results follow the one given by Ivanov and Olshanski for Plancherel measures; hence, one uses a "method of noncommutative moments''.
Complete list of metadata

Cited literature [10 references]  Display  Hide  Download
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Tuesday, October 13, 2015 - 3:05:30 PM
Last modification on : Saturday, January 15, 2022 - 3:57:37 AM
Long-term archiving on: : Thursday, April 27, 2017 - 12:27:39 AM


Publisher files allowed on an open archive



Pierre-Loïc Méliot. Kerov's central limit theorem for Schur-Weyl and Gelfand measures (extended abstract). 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.669-680, ⟨10.46298/dmtcs.2943⟩. ⟨hal-01215045⟩



Record views


Files downloads