Perturbation theory for the Rosenzweig-Porter matrix model

摘要

We study a generalized matrix ensemble (the Rosenzweig-Porter model) which contains a parameter mu. This parameter scales with the matrix size N as mu similar to N-alpha. Depending on the value of the exponent alpha, three distinct level statistics are possible, in the N --> infinity limit. We show that a rather complete understanding of level correlations can be gained from the standard diagrammatic perturbation theory. [References: 15]