Roots of generalised Hermite polynomials when both parameters are large

We study the roots of generalised Hermite polynomials Hm,n when both m and n are large. prove that roots, appropriately rescaled, densely fill a bounded quadrilateral region, called elliptic organise themselves on deformed rectangular grid, as was numerically observed by Clarkson. describe region grid in terms integrals their degenerations.