A CLT for Plancherel representations of the infinite-dimensional unitary group

2012/03/14 by Alexei Borodin, Borodin, Alexei, Alexey Bufetov +1 · 1 citation
Chemistry · Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #Probability (math.PR) #Random Matrices and Applications #Representation Theory (math.RT) #advanced mathematical theories #math-ph #math.MP #math.PR #math.RT

paper · pdf · doi:10.48550/arxiv.1203.3010

12 pages

arxiv created 2012/03/14 · openalex publication_date 2012/03/14 · arxiv updated 2012/03/15 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

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. This note is an announcement, proofs will appear elsewhere.

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• Plancherel representations of U(∞) and correlated Gaussian Free Fields

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