Electronic Communications in Probability

Random walk on the randomly-oriented Manhattan lattice

Sean Ledger, Bálint Tóth, and Benedek Valkó

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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.

Article information

Electron. Commun. Probab., Volume 23 (2018), paper no. 43, 11 pp.

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

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Zentralblatt MATH identifier

Primary: 82C41: Dynamics of random walks, random surfaces, lattice animals, etc. [See also 60G50]

Random walks in random environment superdiffusivity

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Ledger, Sean; Tóth, Bálint; Valkó, Benedek. Random walk on the randomly-oriented Manhattan lattice. Electron. Commun. Probab. 23 (2018), paper no. 43, 11 pp. doi:10.1214/18-ECP144. https://projecteuclid.org/euclid.ecp/1532505674

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