# Expected lengths and distribution functions for Young diagrams in the hook

Authors
Type
Preprint
Publication Date
Jun 23, 2005
Submission Date
Jun 23, 2005
Identifiers
arXiv ID: math/0506469
Source
arXiv
We consider $\beta$--Plancherel measures \cite{Ba.Ra.} on subsets of partitions -- and their asymptotics. These subsets are the Young diagrams contained in a $(k,\ell)$--hook, and we calculate the asymptotics of the expected shape of these diagrams, relative to such measures. We also calculate the asymptotics of the distribution function of the lengths of the rows and the columns for these diagrams. This might be considered as the restriction to the $(k,\ell)$--hook of the fundamental work of Baik, Deift and Johansson \cite{B.D.J.1}. The above asymptotics are given here by ratios of certain Selberg-type multi--integrals.