Plancherel representations of \(U(\infty)\) and correlated Gaussian free fields

DOI10.1215/00127094-2795217zbMath1322.60062arXiv1301.0511OpenAlexW3106240418MaRDI QIDQ742561

Alexei Borodin, Alexey I. Bufetov

Publication date: 18 September 2014

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.0511

zbMATH Keywords

random matricescentral limit theoremheight functioninfinite-dimensional unitary groupGaussian free fieldsPlancherel representations

Mathematics Subject Classification ID

Random fields (60G60) Gaussian processes (60G15) Central limit and other weak theorems (60F05) Random matrices (probabilistic aspects) (60B20) Combinatorial probability (60C05) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15) Analysis on and representations of infinite-dimensional Lie groups (22E66)

Related Items (11)

Nearest neighbor Markov dynamics on Macdonald processes ⋮ Three-dimensional Gaussian fluctuations of non-commutative random surfaces along time-like paths ⋮ On global fluctuations for non-colliding processes ⋮ Spherical representations of \(C^\ast\)-flows. II: Representation system and quantum group setup ⋮ General β-Jacobi Corners Process and the Gaussian Free Field ⋮ Multiplicative characters and Gaussian fluctuation limits ⋮ Integrable probability: from representation theory to MacDonald processes ⋮ Law of large numbers and central limit theorems through Jack generating functions ⋮ Fluctuations of particle systems determined by Schur generating functions ⋮ Fourier transform on high-dimensional unitary groups with applications to random tilings ⋮ Limit shapes for growing extreme characters of \(U(\infty)\)

Cites Work

• A CLT for Plancherel representations of the infinite-dimensional unitary group
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• The boundary of the Gelfand-Tsetlin graph: A new approach
• Asymptotics of Plancherel measures for the infinite-dimensional unitary group
• Représentations factorielles de type \(II_1\) de \(U(\infty)\)
• Limit shapes for growing extreme characters of \(U(\infty)\)
• Asymptotics of Plancherel-type random partitions
• Entropy of Schur-Weyl measures
• Gaussian free fields for mathematicians
• CLT for spectra of submatrices of Wigner random matrices
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• Symmetry, Representations, and Invariants
• On the Generating Function of a Doubly Infinite, Totally Positive Sequence
• Discrete orthogonal polynomial ensembles and the Plancherel measure
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