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.
關聯:
Random Matrices: Theory and Applications 7(4), 1840002(20 pages)