Spectral statistics of multiparametric Gaussian ensembles with chiral symmetry

The statistics of chiral matrix ensembles with uncorrelated but multivariate Gaussian distributed elements is intuitively expected to be driven by many parameters. Contrary to intuition, however, our theoretical analysis reveals the existence of a single parameter, a function of all ensemble parameters, which governs the dynamics of spectral statistics. The analysis not only extends the formulation (known as complexity parameter formulation) for Hermitian ensembles without chirality to those with it but also reveals the underlying connection between chiral complex systems with seemingly different system conditions as well as between other complex systems, e.g., multiparametric Wishart ensembles as well as generalized Calogero-Sutherland Hamiltonians.