Random Young diagrams in a Rectangular Box

Dan Beltoft (1) , Cédric Boutillier (2, 3) , Nathanaël Enriquez (2, 4)

1 IMF - Institut for Matematiske Fag
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 DMA - Département de Mathématiques et Applications - ENS Paris
4 MODAL'X - Modélisation aléatoire de Paris X

We exhibit the limit shape of random Young diagrams having a distribution proportional to the exponential of their area, and confined in a rectangular box. The Ornstein-Uhlenbeck bridge arises from the fluctuations around the limit shape.

Keywords: Young diagrams; Gauss polynomials; Ornstein-Uhlenbeck process

Domains: Probability [math.PR]; Combinatorics [math.CO]

Dan Beltoft, Cédric Boutillier, Nathanaël Enriquez. Random Young diagrams in a Rectangular Box. Moscow Mathematical Journal, 2012, 12 (4), pp.719-745. ⟨hal-00508535v2⟩