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arXiv · 2610.40464

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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Mark Holmes, Thomas S. Salisbury. 2026-10-29. The velocity is deterministic in random walk in 2-valued i.i.d. random environment. https://arxiv.org/abs/2610.40464

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