This article is cited in 8 papers

Random Young Diagrams in a Rectangular Box

Dan Beltoft^a, Cédric Boutillier^bc, Nathanaël Enriquez<sup>d

a</sup> Aarhus University, Department of Math. Sciences, Ny Munkegade 118, 8000, Aarhus C, Denmark
^b Université Pierre et Marie Curie, Laboratoire LPMA, 4 place Jussieu 75005, Paris, France
^c École Normale Supérieure, DMA, 45 rue d’Ulm 75005 Paris, France
^d Université Paris-Ouest, Laboratoire MODAL’X, 200 Av. de la République 92001, Nanterre, France

Abstract: We exhibit the limit shape of random Young diagrams having a distribution proportional to the exponential of their area (grand-canonical ensemble), and confined in a rectangular box. The Ornstein–Uhlenbeck bridge arises from the fluctuations around the limit shape. The fluctuations for the unconfined case lead to a two-sided stationary Ornstein–Uhlenbeck process.

Key words and phrases: Young diagrams, Gauss polynomials, Ornstein–Uhlenbeck process.

MSC: 60C05, 60F17, 05A10, 05A15, 05A30

Received: October 26, 2010; in revised form December 15, 2011

Language: English

DOI: 10.17323/1609-4514-2012-12-4-719-745

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