Electronic Communications in Probability

Random walk on the randomly-oriented Manhattan lattice

Sean Ledger, Bálint Tóth, and Benedek Valkó

Full-text: Open access

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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1532505674

Digital Object Identifier
doi:10.1214/18-ECP144

Mathematical Reviews number (MathSciNet)
MR3841404

Zentralblatt MATH identifier
1397.82046

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

Keywords
Random walks in random environment superdiffusivity

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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