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.
Citation
Sean Ledger. Bálint Tóth. Benedek Valkó. "Random walk on the randomly-oriented Manhattan lattice." Electron. Commun. Probab. 23 1 - 11, 2018. https://doi.org/10.1214/18-ECP144
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