TY - JOUR
AU1 - Forrester, P.
AU2 - Ipsen, J.
AU3 - Liu, Dang-Zheng
AB - 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. Explicit expressions for the bi-orthogonal functions as well as the correlation kernel are provided. Scaling the latter near the origin gives a limiting kernel involving Meijer G-functions, and the functional form of the global density is calculated. As a part of this study, we introduce a new matrix transformation which maps the space of polynomial ensembles onto itself. This matrix transformation is closely related to the so-called hyperbolic Harish-Chandra–Itzykson–Zuber integral.
TI - Matrix Product Ensembles of Hermite Type and the Hyperbolic Harish-Chandra–Itzykson–Zuber Integral
JF - Annales Henri Poincaré
DO - 10.1007/s00023-018-0654-x
DA - 2018-02-24
UR - https://www.deepdyve.com/lp/springer-journals/matrix-product-ensembles-of-hermite-type-and-the-hyperbolic-harish-0JQB0zdSK9
SP - 1307
EP - 1348
VL - 19
IS - 5
DP - DeepDyve
ER -