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Plancherel representations of U(∞) and correlated Gaussian free fields

Author(s)
Borodin, Alexei; Bufetov, Alexey
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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.
Date issued
2014-08
URI
http://hdl.handle.net/1721.1/92824
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Duke Mathematical Journal
Publisher
Duke University Press
Citation
Borodin, Alexei, and Alexey Bufetov. “Plancherel Representations of U(∞) and Correlated Gaussian Free Fields.” Duke Mathematical Journal 163, no. 11 (August 2014): 2109–2158.
Version: Original manuscript
ISSN
0012-7094

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