Transition from Poisson to Gaussian unitary statistics:  The two-point correlation function

We study the two-point correlation function in an ensemble of Hermitian random matrices (the Rosenzweig-Porter matrix model). This ensemble is not invariant under unitary transformations and it exhibits a crossover from Poisson to Wigner-Dyson statistics. Extending the recent method of Brezin and Hikami, we derive an expression for the two-point function (in the limit of infinite matrix size) and analyze some limiting cases.