A CLT Plancherel representations of the infinite-dimensional unitary group
Author(s)Bufetov, Alexey; Borodin, Alexei
A CLT for Plancherel representations of the infinite-dimensional unitary group
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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.
Original Manuscript March 14, 2012
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Journal of Mathematical Sciences
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.