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We study how the Hurst exponent $alpha$ depends on the fraction $f$ of the total time $t$ remembered by non-Markovian random walkers that recall only the distant past. We find that otherwise nonpersistent random walkers switch to persistent behavior when inflicted with significant memory loss. Such memory losses induce the probability density function of the walkers position to undergo a transition from Gaussian to non-Gaussian. We interpret these findings of persistence in terms of a breakdown of self-regulation mechanisms and discuss their possible relevance to some of the burdensome behavioral and psychological symptoms of Alzheimers disease and other dementias.
We investigate a recently proposed non-Markovian random walk model characterized by loss of memories of the recent past and amnestically induced persistence. We report numerical and analytical results showing the complete phase diagram, consisting of
In this minireview we present the main results regarding the transport properties of stochastic movement with relocations to known positions. To do so, we formulate the problem in a general manner to see several cases extensively studied during the l
We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a Levy walk process, often used to
We introduce a heterogeneous continuous time random walk (HCTRW) model as a versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as porous or disordered media, multiscale or crowded environmen
The problem of how many trajectories of a random walker in a potential are needed to reconstruct the values of this potential is studied. We show that this problem can be solved by calculating the probability of survival of an abstract random walker