A q-generalization of the Toda equations for the q-Laguerre/Hermite orthogonal polynomials
arXiv:1805.00818 · doi:10.1142/S2010326318400026
Abstract
Based on the motivation of generalizing the correspondence between the Lax equation for the Toda lattice and the deformation theory of the orthogonal polynomials, we derive a q-deformed version of the Toda equations for both q-Laguerre/Hermite ensembles, and check the compatibility with the quadratic relation.
20 pages. arXiv admin note: substantial text overlap with arXiv:1612.09039