Average characteristic polynomials for multiple orthogonal polynomial ensembles KU Leuven
Multiple orthogonal polynomials (MOP) are a non-definite version of matrix orthogonal polynomials. They are described by a Riemann Hilbert matrix Y consisting of four blocks Y-1,Y-1, Y-1,Y-2, Y-2,Y-1 and Y-2,Y-2. In this paper, we show that det Y-1,Y-1 (det Y-1,Y-2) equals the average characteristic polynomial (average inverse characteristic polynomial, respectively) over the probabilistic ensemble that is associated to the MOP. In this way we ...