Anomalous Diffusion and Continuous-Time Random Walks

In the previous Chapter we have reviewed different classical models of movement and have explored how they behave in the large time asymptotic regime. The emphasis has been put in showing the working methods and characteristics of the different levels of description (macroscopic, mesoscopic and microscopic). Next we shall show how this differentiation helps us when introducing more advanced concepts like that of memory in the transport processes. Memory has also been considered in the previous chapter, but only in a very elementary way through correlated (persistent) movement in which the direction of motion can be changed according to the current state (e.g. the current direction) of the individual. Nevertheless, the effects that the whole previous history of the trajectory may have on the motion process have not been considered yet.

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