A CLT Plancherel representations of the infinite-dimensional unitary group
Name
Borodin_A CLT plancherel.pdf
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160.43 KB
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Author(s)
Bufetov, Alexey
Borodin, Alexei
Alternative Title
A CLT for Plancherel representations of the infinite-dimensional unitary group
Date Issued
April 2013
Journal
Journal of Mathematical Sciences
Publisher
Springer-Verlag
Citation
Borodin, A., and A. Bufetov. “A CLT Plancherel representations of the infinite-dimensional unitary group.” Journal of Mathematical Sciences 190, no. 3 (April 20, 2013): 419-426.
Version
Original manuscript
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 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 submatrices of Wigner Hermitian random matrices.
Description
Original Manuscript March 14, 2012
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s10958-013-1257-1
