Amnestically induced persistence in random walks

TL;DR

This paper investigates how partial memory loss in non-Markovian random walks causes a transition from Gaussian to non-Gaussian behavior and induces persistence, with implications for understanding dementia-related symptoms.

Contribution

It reveals that memory loss can induce persistence and non-Gaussian distributions in non-Markovian random walks, linking stochastic behavior to neurological conditions.

Findings

Memory loss induces persistent behavior in non-Markovian random walks.

Transition from Gaussian to non-Gaussian probability density functions occurs with increased memory loss.

Memory impairment affects self-regulation mechanisms in stochastic models.

Abstract

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 walker's 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 Alzheimer's disease and other dementias.