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Gaussian processes in complex media: new vistas on anomalous diffusion
Normal or Brownian diffusion is historically identified by the linear growth in time of the variance and by a Gaussian shape of the displacement distribution. Processes departing from the at least one of the above conditions ...
Finite-energy Lévy-type motion through heterogeneous ensemble of Brownian particles
Complex systems are known to display anomalous diffusion, whose signature is a space/time scaling $x \sim t^\delta$ with $\delta \neq 1/2$ in the probability density function (PDF). Anomalous diffusion can emerge jointly ...
Fractional kinetics in random/complex media
In this chapter, we consider a randomly-scaled Gaussian process and discuss a number of applications to model fractional diffusion. Actually, this approach can be understood as a Gaussian diffusion in a medium characterized ...