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PreprintCC BY 4.0arXiv

The velocity is deterministic in random walk in 2-valued i.i.d. random environment

  • Mark Holmes
  • Thomas S. Salisbury
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Abstract

We prove that the limiting velocity for (nearest-neighbour) random walk in i.i.d. random environment is deterministic when the local environment is supported on two points. No ellipticity is assumed. The proof uses a clever adaption (suggested by ChatGPT) of coupling arguments previously developed by the authors. It extends to i.i.d. environments where the local environments are mixtures of two such points.

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Cite

BibTeXRIS
BibTeX
@misc{holmes2026velocity,
  title = {{The velocity is deterministic in random walk in 2-valued i.i.d. random environment}},
  author = {Mark Holmes and Thomas S. Salisbury},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.40464},
  eprint = {2610.40464},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.40464},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The velocity is deterministic in random walk in 2-valued i.i.d. random environment
AU  - Mark Holmes
AU  - Thomas S. Salisbury
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.40464
UR  - https://arxiv.org/abs/2610.40464
AB  - We prove that the limiting velocity for (nearest-neighbour) random walk in i.i.d. random environment is deterministic when the local environment is supported on two points. No ellipticity is assumed. The proof uses a clever adaption (suggested by ChatGPT) of coupling arguments previously developed by the authors. It extends to i.i.d. environments where the local environments are mixtures of two such points.
ER  -