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Geodesics in first-passage percolation cross any pattern

Abstract : In first-passage percolation, one places nonnegative i.i.d. random variables (T (e)) on the edges of Z d. A geodesic is an optimal path for the passage times T (e). Consider a local property of the time environment. We call it a pattern. We investigate the number of times a geodesic crosses a translate of this pattern. Under mild conditions, we show that, apart from an event with exponentially small probability, this number is linear in the distance between the extremities of the geodesic.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03630139
Contributor : Antonin Jacquet Connect in order to contact the contributor
Submitted on : Monday, April 4, 2022 - 6:15:54 PM
Last modification on : Wednesday, April 6, 2022 - 3:32:28 AM

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  • HAL Id : hal-03630139, version 1
  • ARXIV : 2204.02021

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Antonin Jacquet. Geodesics in first-passage percolation cross any pattern. 2022. ⟨hal-03630139⟩

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