Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Classical discrete symplectic ensembles on the linear and exponential lattice: skew orthogonal polynomials and correlation functions


Authors: Peter J. Forrester and Shi-Hao Li
Journal: Trans. Amer. Math. Soc. 373 (2020), 665-698
MSC (2010): Primary 15B52; Secondary 33E20, 15A15
DOI: https://doi.org/10.1090/tran/7957
Published electronically: September 23, 2019
MathSciNet review: 4042888
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 action on the corresponding (discrete or $ q$) orthogonal polynomials.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 15B52, 33E20, 15A15

Retrieve articles in all journals with MSC (2010): 15B52, 33E20, 15A15


Additional Information

Peter J. Forrester
Affiliation: School of Mathematical and Statistics, ARC Centre of Excellence for Mathematical and Statistical Frontiers, The University of Melbourne, Victoria 3010, Australia
Email: pjforr@unimelb.edu.au

Shi-Hao Li
Affiliation: School of Mathematical and Statistics, ARC Centre of Excellence for Mathematical and Statistical Frontiers, The University of Melbourne, Victoria 3010, Australia
Email: shihao.li@unimelb.edu.au

DOI: https://doi.org/10.1090/tran/7957
Keywords: Classical discrete symplectic ensemble, skew orthogonal polynomials, correlation kernel
Received by editor(s): February 25, 2019
Received by editor(s) in revised form: July 18, 2019
Published electronically: September 23, 2019
Additional Notes: The first author acknowledges partial support from ARC grant DP170102028.
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)
Article copyright: © Copyright 2019 American Mathematical Society