Abstract: Spectral properties of random matrices have many applications in physics, ranging from nuclear physics to disordered systems. This ubiquity can be traced back to the universality of spectral properties: whatever the distribution of the entries are, the spectral observables obey some universal laws when the size of the matrices become large. A simple example is Wigner's semi-circle law that describes the density of eigenvalues for a hermitian matrix whose entries are independent and identically distributed (iid). We extend it beyond the iid case, provided the cumulants obey a simple power law bound in the size of the matrix. To derive this result, we use the replica technique and a renormalisation group equation for the replica effective action. This is joint work with Vu Dinh Long (student at Ecole Polytechnique) and Adrian Tanasa (LABRI, Bordeaux).