Conferencia: The large deviation approach to statistical physics
I will give in this talk a basic overview of the theory of large deviations and of its applications in statistical physics. In the first part, I will discuss the basics of this theory and its historical sources, which can be traced back in mathematics to Cramer (1938), Sanov (1960) and Varadhan (1970s) and, on the physics side, to Einstein (1910) and Boltzmann (1877). In the second part, I will discuss how the theory has been applied in recent years to study various equilibrium, nonequilibrium, and complex systems, such as interacting particle systems, turbulent flows, and random graphs, among many other examples. Some of these applications have been studied by researchers in the statistical physics group in Granada.