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

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Author
Forrester, PJ; Li, S-HDate
2020-01-01Source Title
Transactions of the American Mathematical SocietyPublisher
AMER MATHEMATICAL SOCAffiliation
School of Mathematics and StatisticsMetadata
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Forrester, P. J. & Li, S. -H. (2020). CLASSICAL DISCRETE SYMPLECTIC ENSEMBLES ON THE LINEAR AND EXPONENTIAL LATTICE: SKEW ORTHOGONAL POLYNOMIALS AND CORRELATION FUNCTIONS. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 373 (1), pp.665-698. https://doi.org/10.1090/tran/7957.Access Status
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https://doi.org/10.1090/tran/7957Abstract
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.
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