  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.
