Residual Diffusivity in Elephant Random Walk Models with Stops

Jiancheng Lyu; Jack Xin; Yifeng Yu

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arXiv · 1705.02711

Residual Diffusivity in Elephant Random Walk Models with Stops

Jiancheng Lyu·Jack Xin·Yifeng Yu

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Abstract

We study the enhanced diffusivity in the so called elephant random walk model with stops (ERWS) by including symmetric random walk steps at small probability $\epsilon$. At any $\epsilon > 0$, the large time behavior transitions from sub-diffusive at $\epsilon = 0$ to diffusive in a wedge shaped parameter regime where the diffusivity is strictly above that in the un-perturbed ERWS model in the $\epsilon \downarrow 0$ limit. The perturbed ERWS model is shown to be solvable with the first two moments and their asymptotics calculated exactly in both one and two space dimensions. The model provides a discrete analytical setting of the residual diffusion phenomenon known for the passive scalar transport in chaotic flows (e.g. generated by time periodic cellular flows and statistically sub-diffusive) as molecular diffusivity tends to zero.

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Jiancheng Lyu, Jack Xin, Yifeng Yu. 2017-05-08. Residual Diffusivity in Elephant Random Walk Models with Stops. https://arxiv.org/abs/1705.02711

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