Utilizzo delle Matrici Random nello studio della 'stabilità-complessità' dei sistemi ecologici

Random matrix theory has found applications in many fields, ranging from physics, number theory and ecology. Forty 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 number of interactions through the use of random matrix theory. However, in natural system pairs of species have well-defined interactions (for example predator-prey, mutualistic or competitive) and several recent works have extended May's results to these relationships and find remarkable differences between different interactions. This master thesis is aimed to critically review these results and present them in unified way using the language of statistical physics.