Theoretical study uncovers asymptotic edge density expansions in Gaussian and Laguerre ensembles, suggesting broader integrable structures across classical random matrix models.
Key Points
Investigate asymptotic expansions of scaled eigenvalue densities at both the soft and hard edges of classical Gaussian and Laguerre random matrix ensembles across multiple symmetry classes.
Applied scalar differential equations satisfied by eigenvalue densities rather than traditional integral representations.
Analyzed soft edge scaling variables across orthogonal, unitary, and symplectic symmetries, extending the framework to Dyson index beta = 6.
Formulated hard edge expansions specifically for the classical Laguerre ensembles.
Isolated the explicit expansion parameter in soft edge scaling variables, providing correction terms that supplement known integrable asymptotics.
Derived explicit correction terms at second order for unitary symmetry and at first order for orthogonal and symplectic symmetry at the Laguerre hard edge.
Demonstrated differential relations indicating that integrable asymptotic features extend generally to classical beta-ensembles.