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arXiv · 1802.01558

Random walk on the randomly-oriented Manhattan lattice

Sean Ledger·Bálint Tóth·Benedek Valkó
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Abstract

In the randomly-oriented Manhattan lattice, every line in $\mathbb{Z}^d$ is assigned a uniform random direction. We consider the directed graph whose vertex set is $\mathbb{Z}^d$ and whose edges connect nearest neighbours, but only in the direction fixed by the line orientations. Random walk on this directed graph chooses uniformly from the $d$ legal neighbours at each step. We prove that this walk is superdiffusive in two and three dimensions. The model is diffusive in four and more dimensions.

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Sean Ledger, Bálint Tóth, Benedek Valkó. 2018-02-05. Random walk on the randomly-oriented Manhattan lattice. https://arxiv.org/abs/1802.01558

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