Residual diffusivity in elephant random walk models with stops

Jiancheng Lyu Jack Xin Yifeng Yu

Statistics Theory and Methods mathscidoc:1912.43899

arXiv preprint arXiv:1705.02711, 2017.5
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 , the large time behavior transitions from sub-diffusive at \epsilon to diffusive in a wedge shaped parameter regime where the diffusivity is strictly above that in the un-perturbed ERWS model in the \epsilon 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 (eg generated by time periodic cellular flows and statistically sub-diffusive) as molecular diffusivity tends to zero.
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  title={Residual diffusivity in elephant random walk models with stops},
  author={Jiancheng Lyu, Jack Xin, and Yifeng Yu},
  booktitle={arXiv preprint arXiv:1705.02711},
Jiancheng Lyu, Jack Xin, and Yifeng Yu. Residual diffusivity in elephant random walk models with stops. 2017. In arXiv preprint arXiv:1705.02711.
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