Irregular parameter dependence of generalized diffusion coefficients based on large deviation statistical analysis

The nonperturbative non-Gaussian characteristics of diffusive motion are examined in the framework of the large deviation statistical theory, where simple extended mapping models showing chaotic diffusion are taken as an example. Furthermore, by rigorously solving the large deviation statistical quantities, it is found that the same type of anomalous, complex control parameter dependence as that for the diffusion coefficient reported by Klages and Dorfman is also observed in the large deviation statistical quantities such as the weighted average, the generalized diffusion coefficient, and the generalized power spectrum densities.