Amplificazione esponenziale di fluttuazioni esponenzialmente rare: un meccanismo universale

Abstract

The Gumbel distribution is an example of universal distribution that characterizes the statistics of extreme values for a wide class of starting distributions, provided with an exponential tail. Recently, the Gumbel distribution has been empirically shown in different physical systems sharing a strong spatial correlation. The connection between the statistics of extreme values and strongly correlated systems is still subject of debate in literature. The aim of this thesis is to investigate, both analytically and numerically, a third alternative, studying the possible emergence of the Gumbel distribution as a universal result of the exponential amplification of the the exponential tails of any other distribution.