Abstract: While large deviation for i.i.d. random variables in the domain of a stable law are classified, the results in the dependent case are very scarce. Optimal stable local large deviation for i.i.d. random variables has only been recently obtained.
In this talk I will explain how to generalize this type of results via analytic arguments to large classes of dependent random variables, with application to systems of interest such as Lorentz gases. The results on local large deviations are joint work with Ian Melbourne and Françoise Pène. Large deviation for the dependent case (with application to Gibbs Markov maps) is joint work with Jonny Imbierski.