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PreprintarXiv licencearXiv

The randomly oriented Manhattan lattice in 2D is transient

  • Ahmed Bou-Rabee
  • Yuval Peres
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Abstract

Independently orient each horizontal and vertical line of ℤ2 by a fair coin. A walker chooses one of the two lines through its current position with equal probability and takes one step in the direction of that line. Redner (1989) introduced this walk as a model of transport in an isotropic random velocity field and predicted that its root-mean-square displacement grows like n2/3. We prove that the walk is transient almost surely. The proof is a short variational argument.

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Cite

BibTeXRIS
BibTeX
@misc{bourabee2026randomly,
  title = {{The randomly oriented Manhattan lattice in 2D is transient}},
  author = {Ahmed Bou-Rabee and Yuval Peres},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.07621},
  eprint = {2609.07621},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07621},
}
RIS
TY  - UNPB
TI  - The randomly oriented Manhattan lattice in 2D is transient
AU  - Ahmed Bou-Rabee
AU  - Yuval Peres
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.07621
UR  - https://arxiv.org/abs/2609.07621
AB  - Independently orient each horizontal and vertical line of ℤ^2 by a fair coin. A walker chooses one of the two lines through its current position with equal probability and takes one step in the direction of that line. Redner (1989) introduced this walk as a model of transport in an isotropic random velocity field and predicted that its root-mean-square displacement grows like n^2/3. We prove that the walk is transient almost surely. The proof is a short variational argument.
ER  -