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.
Received:October 26, 2010; in revised form December 15, 2011
\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://mathscinet.ams.org/mathscinet-getitem?mr=3076852}
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Linking options:
https://www.mathnet.ru/eng/mmj478
https://www.mathnet.ru/eng/mmj/v12/i4/p719
This publication is cited in the following 8 articles:
Stephen Melczer, Greta Panova, Robin Pemantle, “Counting Partitions inside a Rectangle”, SIAM J. Discrete Math., 34:4 (2020), 2388
Tadahisa Funaki, SpringerBriefs in Probability and Mathematical Statistics, Lectures on Random Interfaces, 2016, 93
Tadahisa Funaki, SpringerBriefs in Probability and Mathematical Statistics, Lectures on Random Interfaces, 2016, 1
Tadahisa Funaki, SpringerBriefs in Probability and Mathematical Statistics, Lectures on Random Interfaces, 2016, 29
Tadahisa Funaki, SpringerBriefs in Probability and Mathematical Statistics, Lectures on Random Interfaces, 2016, 111
Tadahisa Funaki, SpringerBriefs in Probability and Mathematical Statistics, Lectures on Random Interfaces, 2016, 81
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
Funaki T., “Equivalence of Ensembles Under Inhomogeneous Conditioning and its Applications to Random Young Diagrams”, J. Stat. Phys., 154:1-2 (2014), 588–609
Citation in format AMSBIB
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