2013/01/03 by Alexei Borodin, Alexey Bufetov
Mathematics · Physics and Astronomy · #math-ph #math.MP #math.PR #math.RT
paper · pdf · doi:10.1215/00127094-2795217
published as Duke Math. J. 163, no. 11 (2014), 2109-2158 · 43 pages
arxiv created 2013/01/03 · arxiv updated 2015/01/14
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. The results of the present work were announced in arXiv:1203.3010.