Geodesics and Wandering Exponents in Brochette First-Passage Percolation

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.