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A considerable number of systems have recently been reported in whichBrownian yet non-Gaussian dynamics was observed. These are processescharacterised by a linear growth in time of the mean squared displacement, yetthe probability density function of the particle displacement is distinctlynon-Gaussian, and often of exponential (Laplace) shape. This apparentlyubiquitous behaviour observed in very different physical systems has beeninterpreted as resulting from diffusion in inhomogeneous environments andmathematically represented through a variable, stochastic diffusioncoefficient. Indeed different models describing a fluctuating diffusivity havebeen studied. Here we present a new view of the stochastic basis describingtime dependent random diffusivities within a broad spectrum of distributions.Concretely, our study is based on the very generic class of the generalisedGamma distribution. Two models for the particle spreading in such randomdiffusivity settings are studied. The first belongs to the class of generalisedgrey Brownian motion while the second follows from the idea of diffusingdiffusivities. The two processes exhibit significant characteristics whichreproduce experimental results from different biological and physical systems.We promote these two physical models for the description of stochastic particlemotion in complex environments.

Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion