Journal article

CLASSICAL DISCRETE SYMPLECTIC ENSEMBLES ON THE LINEAR AND EXPONENTIAL LATTICE: SKEW ORTHOGONAL POLYNOMIALS AND CORRELATION FUNCTIONS

Peter J Forrester, Shi-Hao Li

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | AMER MATHEMATICAL SOC | Published : 2020

Abstract

The eigenvalue probability density function for symplectic invariant random matrix ensembles can be generalized to discrete settings involving either a linear or an exponential lattice. The corresponding correlation functions can be expressed in terms of certain discrete and q skew orthogonal polynomials, respectively. We give a theory of both of these classes of polynomials, and the correlation kernels determining the correlation functions, in the cases in which the weights for the corresponding discrete unitary ensembles are classical. Crucial for this are certain difference operators which relate the relevant symmetric inner products to the skew symmetric ones, and have a tridiagonal acti..

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University of Melbourne Researchers

Grants

Awarded by ARC grant


Funding Acknowledgements

The first author acknowledges partial support from ARC grant DP170102028.r This work was part of a research program supported by the Australian Research Council (ARC) through the ARC Centre of Excellence for Mathematical and Statistical frontiers (ACEMS).