Random Matrix Product of Hermite-type
Speaker(s): Dang-Zheng Liu(University of Science and Technology of China)
Time: 15:00-16:00 September 1, 2017
Venue: Room 78201, Jingchunyuan 78, BICMR
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 find an explicit expression of the joint probability density function as a bi-orthogonal ensemble. As an interesting example, we focus on the product of GUE and LUE matrices and provide explicit expressions both for the bi-orthogonal functions and the correlation kernel. Then a new double-side kernel is found at the origin, which is slightly different from the Bessel kernel.