Moderate deviation principles for eigenvalues of ββ-Hermite and ββ-Laguerre ensembles with β→∞β→∞

In this paper we consider the moderate deviation principles for the joint eigenvalues of ββ-Hermite and ββ-Laguerre ensembles when β→∞β→∞ with dimensions kk fixed. Our proofs rely on finite dimensional matrix perturbation theory and some exponential equivalence estimates.