Large deviations for biorthogonal ensembles and variational formulation for the Dykema-Haagerup distribution

Abstract

This note provides a large deviation principle for a class of biorthogonal ensembles. We extend the results of Eichelsbacher, Sommerauer and Stolz to a more general type of interactions. In particular, our result covers the case of the singular values of lower triangular random matrices with independent entries introduced by Cheliotis and implies a variational formulation for the Dykema–Haagerup distribution.