Robustness of RP spectral properties under distribution modifications

Determine the extent to which the spectral properties of the Rosenzweig–Porter random matrix ensemble are robust when the distribution of the Hamiltonian matrix elements is modified, including deviations from the usual independent and identically distributed assumptions for the diagonal and off-diagonal entries, in order to assess the universality of its phase diagram and spectral correlators.

Background

The Rosenzweig–Porter (RP) ensemble is a widely studied model for non-ergodic extended (fractal) phases, typically defined as the sum of a diagonal matrix with i.i.d. entries and a Gaussian random matrix. Many recent results point to universality in its spectral properties, but realistic systems often violate independence or have different entry distributions.

The paper introduces the Wishart–RP ensemble to begin probing robustness beyond uncorrelated Gaussian off-diagonal entries, showing superuniversal behavior for the level compressibility in the intermediate phase. The broader question remains to characterize robustness across modifications to the entry distributions themselves.