Moscow Mathematical Journal

Volume 12, Issue 4, October–December 2012 pp. 719–745.

Random Young Diagrams in a Rectangular Box

Authors: Dan Beltoft (1), Cédric Boutillier (2, 3), and Nathanaël Enriquez (4)
Author institution: (1) Aarhus University, Department of Math. Sciences, Ny Munkegade 118, 8000 Aarhus C, Denmark,
(2) Université Pierre et Marie Curie, Laboratoire LPMA, 4 Place Jussieu 75005 Paris, France,
(3) École Normale Supérieure, DMA, 45 rue d'Ulm 75005 Paris, France,
(4) Université Paris-Ouest, Laboratoire MODAL'X, 200 Av. de la République 92001 Nanterre, France
Summary: 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.

2010 Mathematics Subject Classification. 60C05, 60F17, 05A10, 05A15, 05A30
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