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Funktsional. Anal. i Prilozhen., 2012, Volume 46, Issue 2, Pages 3–16 (Mi faa3075)  

This article is cited in 4 scientific papers (total in 4 papers)

A Central Limit Theorem for Extremal Characters of the Infinite Symmetric Group

A. I. Bufetov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The asymptotic behavior of the lengths of the first rows and columns in the random Young diagrams corresponding to extremal characters of the infinite symmetric group is studied. We consider rows and columns with linear growth in $n$ and prove a central limit theorem for their lengths in the case of distinct Thoma parameters. We also prove a more precise statement relating the growth of rows and columns of Young diagrams to a simple independent random sampling model.

Keywords: infinite symmetric group, extremal characters, Young diagrams

DOI: https://doi.org/10.4213/faa3075

Full text: PDF file (232 kB)
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English version:
Functional Analysis and Its Applications, 2012, 46:2, 83–93

Bibliographic databases:

UDC: 519.21
Received: 20.04.2011

Citation: A. I. Bufetov, “A Central Limit Theorem for Extremal Characters of the Infinite Symmetric Group”, Funktsional. Anal. i Prilozhen., 46:2 (2012), 3–16; Funct. Anal. Appl., 46:2 (2012), 83–93

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Bufetov A. Petrov L., “Law of Large Numbers For Infinite Random Matrices Over a Finite Field”, Sel. Math.-New Ser., 21:4 (2015), 1271–1338  crossref  mathscinet  zmath  isi  elib  scopus
    2. Bufetov A., Gorin V., “Stochastic Monotonicity in Young Graph and Thoma Theorem”, Int. Math. Res. Notices, 2015, no. 23, 12920–12940  crossref  mathscinet  zmath  isi  scopus
    3. Benaych-Georges F., Houdre C., “Gue Minors, Maximal Brownian Functionals and Longest Increasing Subsequences in Random Words”, Markov Process. Relat. Fields, 21:1 (2015), 109–126  mathscinet  zmath  isi  elib
    4. O'Donnell R., Wright J., “Efficient Quantum Tomography II”, Stoc'17: Proceedings of the 49Th Annual Acm Sigact Symposium on Theory of Computing, Annual Acm Symposium on Theory of Computing, eds. Hatami H., McKenzie P., King V., Assoc Computing Machinery, 2017, 962–974  crossref  mathscinet  zmath  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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