Spectral density of Wishart matrices and the replica method

Abstract

Random matrix theory provides a powerful framework for understanding universal features of complex systems, especially in the large-size limit. In this work, we study the spectral density of Wishart-Laguerre random matrices using the Edwards-Jones formula. We reinterpret the averaged quantity in the Edwards-Jones formula as the partition function of a disordered system and apply tools from statistical physics. Our results illustrate how techniques from statistical physics of disordered systems naturally extend to random matrix theory, offering physical insight and analytical methods for exploring spectral properties in complex systems