Classical skew orthogonal polynomials in a two-component log-gas with charges 1 and 2
Peter J Forrester, Shi-Hao Li
ADVANCES IN MATHEMATICS | ACADEMIC PRESS INC ELSEVIER SCIENCE | Published : 2021
There is a two-component log-gas system with Boltzmann factor which provides an interpolation between the eigenvalue probability density function (PDF) for β=1 and β=4 invariant random matrix ensembles. Its solvability relies on the construction of particular skew orthogonal polynomials, with the skew inner product a linear combination of the β=1 and β=4 inner products, each involving weight functions. For suitably related classical weight functions, we seek to express the skew orthogonal polynomials as linear combinations of the underlying orthogonal polynomials. It is found that in each case (Gaussian, Laguerre, Jacobi and generalised Cauchy) the coefficients can be expressed in terms of h..View full abstract
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Awarded by ARC
This work is part of a research program supported by the Australian Research Council (ARC) through the ARC Centre of Excellence for Mathematical and Statistical frontiers (ACEMS). PJF also acknowledges partial support from ARC grant DP170102028. S.-H. Li would like to thank ZiF, University of Bielefeld for their generous support when he attended the summer school `Randomness in Physics and Mathematics: From Stochastic Processes to Networks', where this work was begun.