Order parameters for unitary ensembles solve the modified KP equation via the Volterra lattice while orthogonal ensembles yield a new integrable chain via the Pfaff lattice, with thermodynamic limits being hydrodynamic-type systems solved by the same semi-discrete dynamical chain.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 479(2272), pp
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Skew-orthogonal polynomials for a quartic Freud weight are written as linear combinations of orthogonal polynomials via new recursive coefficient relations; even and odd degrees separately become quasi-orthogonal families for two semi-classical Laguerre weights, with the first closed recursions that
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Random matrix ensembles and integrable differential identities
Order parameters for unitary ensembles solve the modified KP equation via the Volterra lattice while orthogonal ensembles yield a new integrable chain via the Pfaff lattice, with thermodynamic limits being hydrodynamic-type systems solved by the same semi-discrete dynamical chain.
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Skew-orthogonal polynomials for a quartic Freud weight: two classes of quasi-orthogonal polynomials
Skew-orthogonal polynomials for a quartic Freud weight are written as linear combinations of orthogonal polynomials via new recursive coefficient relations; even and odd degrees separately become quasi-orthogonal families for two semi-classical Laguerre weights, with the first closed recursions that