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

TL;DR

This paper analyzes the transition in spectral statistics of the Rosenzweig-Porter random matrix model from Poisson to Gaussian Unitary, providing exact two-point correlation functions and asymptotic formulas near the limits.

Contribution

It offers an exact computation of the two-point correlation function for the model and describes the asymptotic behavior near the Poisson and Gaussian limits.

Findings

Exact two-point correlation function derived for the model.

Asymptotic formulas characterize the transition near the limits.

Provides insights into spectral statistics interpolation.

Abstract

We consider the Rosenzweig-Porter model of random matrix which interpolates between Poisson and gaussian unitary statistics and compute exactly the two-point correlation function. Asymptotic formulas for this function are given near the Poisson and gaussian limit.