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Zapiski Nauchnykh Seminarov POMI, 2012, Volume 403, Pages 19–34 (Mi znsl5246)  
This article is cited in 3 scientific papers (total in 3 papers)

A central limit theorem for Plancherel representations of the infinite-dimensional unitary group

A. M. Borodinab, A. I. Bufetovca

a Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia
b Massachusetts Institute of Technology, Department of Mathematics, Cambridge, MA, USA
c Independent University of Moscow, Moscow, Russia
Full-text PDF (290 kB) Citations (3)
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Abstract: We study the asymptotics of traces of (noncommutative) monomials formed by the images of certain elements of the universal enveloping algebra of the infinite-dimensional unitary group in its Plancherel representations. We prove that they converge to (commutative) moments of a Gaussian process which can be viewed as a collection of simply yet nontrivially correlated two-dimensional Gaussian free fields. The limiting process has previously arisen via the global scaling limit of spectra for submatrices of Wigner Hermitian random matrices. This note is an announcement, proofs will appear elsewhere.
Key words and phrases: infinite-dimensional unitary group, Plancherel representation, signature.
Received: 31.05.2012
English version:
Journal of Mathematical Sciences (New York), 2013, Volume 190, Issue 3, Pages 419–426
DOI: https://doi.org/10.1007/s10958-013-1257-1
Bibliographic databases:
Document Type: Article
UDC: 512.815+519.214
Language: Russian
Citation: A. M. Borodin, A. I. Bufetov, “A central limit theorem for Plancherel representations of the infinite-dimensional unitary group”, Representation theory, dynamical systems, combinatorial methods. Part XXI, Zap. Nauchn. Sem. POMI, 403, POMI, St. Petersburg, 2012, 19–34; J. Math. Sci. (N. Y.), 190:3 (2013), 419–426
Citation in format AMSBIB
\Bibitem{BorBuf12}
\by A.~M.~Borodin, A.~I.~Bufetov
\paper A central limit theorem for Plancherel representations of the infinite-dimensional unitary group
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXI
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 403
\pages 19--34
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5246}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3029578}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 190
\issue 3
\pages 419--426
\crossref{https://doi.org/10.1007/s10958-013-1257-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84880641710}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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