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

TL;DR

This paper establishes a large deviations principle for biorthogonal ensembles, extending previous results to more general interactions and deriving a variational formulation for the Dykema-Haagerup distribution as a limit law.

Contribution

It extends large deviations results to broader biorthogonal ensembles and provides a variational characterization of the Dykema-Haagerup distribution.

Findings

Large deviations principle established for a class of biorthogonal ensembles.

Extension of previous results to more general interaction types.

Variational formulation derived for the Dykema-Haagerup distribution.

Abstract

This note provides a large deviations principle for a class of biorthogonal ensembles. We extend the results of Eichelsbacher, Sommerauer and Stotlz to more general type of interactions. Our result covers the case of the singular values of lower triangular random matrices with independent entries introduced by Cheliotis. In particular, we obtain as a consequence a variational formulation for the Dykema-Haagerup as it is the limit law for the singular values of lower triangular matrices with i.i.d. complex Gaussian entries.