Abstract
Non-Markovian random walkers that recall only a fraction $f$ of the total time $t$ are studied. It is shown that otherwise nonpersistent random walkers switch to persistent behavior when inflicted with significant memory loss when only the distant past is remembered. Such memory losses induce the probability density function of the walker's position to undergo a transition from Gaussian to non-Gaussian. These findings of persistence are interpreted in terms of a breakdown of self-regulation mechanisms and their possible relevance to some of the burdensome behavioral and psychological symptoms of Alzheimer's disease and other dementias are also discussed. Part of this work has recently been published in Physical Review Letters (J. C. Cressoni, Marco Antonio Alves da Silva, and G. M. Viswanathan, PRL 98, 070603, (2007)).
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