Transformations of polynomial ensembles
arXiv:1501.05506
Abstract
A polynomial ensemble is a probability density function for the position of real particles of the form , for certain functions . Such ensembles appear frequently as the joint eigenvalue density of random matrices. We present a number of transformations that preserve the structure of a polynomial ensemble. These transformations include the restriction of a Hermitian matrix by removing one row and one column, a rank-one modification of a Hermitian matrix, and the extension of a Hermitian matrix by adding an extra row and column with complex Gaussians.
15 pages, references added, reorganization of some of the proofs