Selberg integrals, super-hypergeometric functions and applications to β-ensembles of random matrices

DOI10.1142/S2010326315500070zbMath1328.15049arXiv1109.4659MaRDI QIDQ3449979

Dang-Zheng Liu, Patrick Desrosiers

Publication date: 30 October 2015

Published in: Random Matrices: Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.4659

zbMATH Keywords

multivariate hypergeometric functionrandom matrix theorybeta-ensemblesSelberg integralsCalogero-Sutherland systemsPfaff-Euler and Kummer transformationssuper-Jack polynomials

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Symmetric functions and generalizations (05E05) Other hypergeometric functions and integrals in several variables (33C70) Random matrices (algebraic aspects) (15B52)

Related Items (7)

New orthogonality relations for super-Jack polynomials and an associated Lassalle-Nekrasov correspondence ⋮ Characteristic polynomials of random truncations: Moments, duality and asymptotics ⋮ Asymptotics for products of characteristic polynomials in classical \(\beta\)-ensembles ⋮ Algebraic analysis of the hypergeometric function \(_1F_1\) of a matrix argument ⋮ Orthogonality of super‐Jack polynomials and a Hilbert space interpretation of deformed Calogero–Moser–Sutherland operators ⋮ From Kajihara's transformation formula to deformed Macdonald-Ruijsenaars and Noumi-Sano operators ⋮ Linear differential equations for the resolvents of the classical matrix ensembles

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