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Mosc. Math. J., 2012, Volume 12, Number 4, Pages 719–745 (Mi mmj478)  

This article is cited in 2 scientific papers (total in 2 papers)

Random Young Diagrams in a Rectangular Box

Dan Beltofta, Cédric Boutillierbc, Nathanaël Enriquezd

a 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.

DOI: https://doi.org/10.17323/1609-4514-2012-12-4-719-745

Full text: http://www.mathjournals.org/.../2012-012-004-004.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 60C05, 60F17, 05A10, 05A15, 05A30
Received: October 26, 2010; in revised form December 15, 2011
Language:

Citation: Dan Beltoft, Cédric Boutillier, Nathanaël Enriquez, “Random Young Diagrams in a Rectangular Box”, Mosc. Math. J., 12:4 (2012), 719–745

Citation in format AMSBIB
\Bibitem{BelBouEnr12}
\by Dan~Beltoft, C\'edric~Boutillier, Nathana\"el~Enriquez
\paper Random Young Diagrams in a Rectangular Box
\jour Mosc. Math.~J.
\yr 2012
\vol 12
\issue 4
\pages 719--745
\mathnet{http://mi.mathnet.ru/mmj478}
\crossref{https://doi.org/10.17323/1609-4514-2012-12-4-719-745}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3076852}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000314341500004}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Funaki T., “Equivalence of Ensembles Under Inhomogeneous Conditioning and its Applications to Random Young Diagrams”, J. Stat. Phys., 154:1-2 (2014), 588–609  crossref  mathscinet  zmath  isi  elib  scopus
    2. Cipriani A., Zeindler D., “the Limit Shape of Random Permutations With Polynomially Growing Cycle Weights”, ALEA-Latin Am. J. Probab. Math. Stat., 12:2 (2015), 971–999  mathscinet  zmath  isi
  • Moscow Mathematical Journal
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