Matrix Product Ensembles of Hermite Type and the Hyperbolic Harish-Chandra–Itzykson–Zuber Integral

• Published in: Annales Henri Poincaré Vol. 19; no. 5; pp. 1307 - 1348
• Main Authors: Forrester, P. J., Ipsen, J. R., Liu, Dang-Zheng
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.05.2018; Springer Nature B.V
• Subjects: Classical and Quantum Gravitation; Dynamical Systems and Ergodic Theory; Eigenvalues; Elementary Particles; Integrals; Mathematical analysis; Mathematical and Computational Physics; Mathematical Methods in Physics; Orthogonal functions; Physics; Physics and Astronomy; Quantum Field Theory; Quantum Physics; Relativity Theory; Theoretical; Transformations (mathematics)

We investigate spectral properties of a Hermitised random matrix product which, contrary to previous product ensembles, allows for eigenvalues on the full real line. We prove that the eigenvalues form a bi-orthogonal ensemble, which reduces asymptotically to the Hermite Muttalib–Borodin ensemble. Ex...