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15 August 2014 Plancherel representations of U() and correlated Gaussian free fields
Alexei Borodin, Alexey Bufetov
Duke Math. J. 163(11): 2109-2158 (15 August 2014). DOI: 10.1215/00127094-2795217

Abstract

We study asymptotics of traces of (noncommutative) monomials formed by 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 that 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.

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Alexei Borodin. Alexey Bufetov. "Plancherel representations of U() and correlated Gaussian free fields." Duke Math. J. 163 (11) 2109 - 2158, 15 August 2014. https://doi.org/10.1215/00127094-2795217

Information

Published: 15 August 2014
First available in Project Euclid: 8 August 2014

zbMATH: 1322.60062
MathSciNet: MR3263029
Digital Object Identifier: 10.1215/00127094-2795217

Subjects:
Primary: 22E66
Secondary: 46L53, 60G15

Rights: Copyright © 2014 Duke University Press

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Vol.163 • No. 11 • 15 August 2014
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