Geodesics and Wandering Exponents in Brochette First-Passage Percolation

Maxime Marivain

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arXiv · 2605.23718

Geodesics and Wandering Exponents in Brochette First-Passage Percolation

Maxime Marivain

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Abstract

We study geodesics in the Brochette first-passage percolation model, where edges on the same axis-parallel line share a common random passage time, inducing long-range dependence. We focus on the maximal transversal deviation H n of geodesics from the origin to ne 1 . We prove existence of geodesics under mild assumptions and establish the order of magnitude of H n depending on the behavior of the passage-time distribution near its infimum. These results yield explicit wandering exponents in this dependent setting.

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Maxime Marivain. 2026-05-22. Geodesics and Wandering Exponents in Brochette First-Passage Percolation. https://arxiv.org/abs/2605.23718

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