Singular Value Statistics of Matrix Products with Truncated Unitary Matrices
Kieburg, Mario
Kieburg
Mario
Kuijlaars, Arno B. J.
Kuijlaars
Arno B. J.
Stivigny, Dries
Stivigny
Dries
We prove that the squared singular values of a fixed matrix multiplied with a truncation of a Haar distributed unitary matrix are distributed by a polynomial ensemble. This result is applied to a multiplication of a truncated unitary matrix with a random matrix. We show that the structure of polynomial ensembles and of certain Pfaffian ensembles is preserved. Furthermore we derive the joint singular value density of a product of truncated unitary matrices and its corresponding correlation kernel which can be written as a double contour integral. This leads to hard edge scaling limits that also include new finite rank perturbations of the Meijer G-kernels found for products of complex Ginibre random matrices.
2016
11
3392-3424
3392-3424
Oxford Univ Press
2016