Soutenance de thèse Pierre Mergny

Random matrix theory has found applications in many fields of physics (disordered systems, stability of dynamical systems, interface models, electronic transport,…) and mathematics (operator algebra, enumerative combinatorics, number theory,…). A recurrent problem in many domains is understanding how the spectra of two random matrices recombine when we perform their sum or product. In this thesis, we study this problem through the prism of spherical integrals and with the help of statistical physics tools. These spherical integrals play the role of the Fourier transform in random matrix theory and their study allows us to understand better the properties of both the limiting spectral density and the largest eigenvalue of these matrix models.