Random diffusivity scenarios behind anomalous non-Gaussian diffusion

Abstract

The standard diffusive spreading, characterized by a Gaussian distribution\nwith mean square displacement that grows linearly with time, can break down,\nfor instance, under the presence of correlations and heterogeneity. In this\nwork, we consider the spread of a population of fractional (long-time\ncorrelated) Brownian walkers, with time-dependent and heterogeneous\ndiffusivity. We aim to obtain the possible scenarios related to these\nindividual-level features from the observation of the temporal evolution of the\npopulation spatial distribution. We develop and discuss the possibility and\nlimitations of this connection for the broad class of self-similar diffusion\nprocesses. Our results are presented in terms of a general framework, which is\nthen used to address well-known processes, such as Laplace diffusion, nonlinear\ndiffusion, and their extensions.\n