1300KbAbstractRandom matrix theory has found applications in many fields, ranging from physics, number theory and ecology. Years ago, in his book entitled emph{Stability and complexity in model ecosystems}, Robert May proved that sufficiently large or complex ecological networks have a probability of persisting that is close to zero, contrary to previous expectations. May analysed large networks in which species interact at random and study analytically the asymptotic stability of ecosystem dynamics as a function of the number of species and…