Plancherel representations of U(∞) and correlated Gaussian free fields
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Borodin_Plancherel representations.pdf
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827.15 KB
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Author(s)
Borodin, Alexei
Bufetov, Alexey
Date Issued
August 2014
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1215/00127094-2795217
