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2018 Random walk on the randomly-oriented Manhattan lattice
Sean Ledger, Bálint Tóth, Benedek Valkó
Electron. Commun. Probab. 23(none): 1-11 (2018). DOI: 10.1214/18-ECP144

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

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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

Information

Received: 5 February 2018; Accepted: 19 June 2018; Published: 2018
First available in Project Euclid: 25 July 2018

zbMATH: 1397.82046
MathSciNet: MR3841404
Digital Object Identifier: 10.1214/18-ECP144

Subjects:
Primary: 82C41

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