Random Young diagrams in a Rectangular Box

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

1 IMF - Institut for Matematiske Fag
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 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.

Mots clés: Young diagrams; Gauss polynomials; Ornstein-Uhlenbeck process

Domaines: Probabilités [math.PR]; Combinatoire [math.CO]

Dan Beltoft, Cédric Boutillier, Nathanaël Enriquez. Random Young diagrams in a Rectangular Box. 2010. ⟨hal-00508535v1⟩