Random walk on the randomlyoriented Manhattan lattice
Abstract
In the randomlyoriented 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2018
 DOI:
 10.48550/arXiv.1802.01558
 arXiv:
 arXiv:1802.01558
 Bibcode:
 2018arXiv180201558L
 Keywords:

 Mathematics  Probability;
 Mathematical Physics
 EPrint:
 11 pages, 2 figures