On a Rosenzweig-Porter-type model
arXiv:2607.02446
The paper analyzes a general Rosenzweig‑Porter random matrix model, studying how eigenvector localization and the eigenstate thermalisation hypothesis evolve as the coupling strength varies, and establishing uniform local laws and the appearance of a mobility edge.
Abstract
We consider a very general Rosenzweig-Porter-type model, , where is an arbitrary Hermitian matrix and is a standard Wigner matrix. We precisely trace the localization properties of the eigenvectors and the eigenstate thermalisation hypothesis (ETH) as the coupling constant interpolates between the trivial case and the fully mean field regime of large . Our results hold uniformly in and , substantially generalising all previous local laws on deformed Wigner matrices even in the mean field regime. Our proof precisely captures the deterministic approximation to the resolvent which exhibits a strongly inhomogeneous structure. As a byproduct, we conclude the emergence of a mobility edge and study the phenomenon of re-entrant localization.
55 pages, 3 figures; v1 -> v2: minor update, added references