Mixing of orthogonal and skew-orthogonal polynomials and its relation to Wilson RMT
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | IOP PUBLISHING LTD | Published : 2012
The unitary Wilson random matrix theory is an interpolation between the chiral Gaussian unitary ensemble and the Gaussian unitary ensemble. This new way of interpolation is also reflected in the orthogonal polynomials corresponding to such a random matrix ensemble. Although the chiral Gaussian unitary ensemble and the Gaussian unitary ensemble are associated with the Dyson index β = 2, the intermediate ensembles exhibit a mixing of orthogonal polynomials and skew-orthogonal polynomials. We consider the Hermitian and the non-Hermitian Wilson random matrix and derive the corresponding polynomials, their recursion relations, ChristoffelDarboux-like formulas, Rodrigues formulas and representatio..View full abstract
I thank Gernot Akemann, Kim Splittorff, Jacobus JM Verbaarschot and Savvas Zafeiropoulos for fruitful discussions and helpful comments. I also acknowledge financial support by the Alexander-von-Humboldt Foundation.