Asymptotics of q-Plancherel measures

Valentin Féray (1) , Pierre-Loïc Méliot (2)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 LIGM - Laboratoire d'Informatique Gaspard-Monge

In this paper, we are interested in the asymptotic size of rows and columns of a random Young diagram under a natural deformation of the Plancherel measure coming from Hecke algebras. The first lines of such diagrams are typically of order $n$, so it does not fit in the context studied by P. Biane and P. \'Sniady. Using the theory of polynomial functions on Young diagrams of Kerov and Olshanski, we are able to compute explicitly the first- and second-order asymptotics of the length of the first rows. Our method works also for other measures, for instance those coming from Schur-Weyl representations.

Mots clés: Asymptotics of Young diagrams; Hecke algebras; deformation of Plancherel measure

Domaines: Théorie des représentations [math.RT]; Probabilités [math.PR]

Valentin Féray, Pierre-Loïc Méliot. Asymptotics of q-Plancherel measures. Probability Theory and Related Fields, 2012, 152 (3-4), pp.589-624. ⟨hal-00446593v2⟩