Pré-Publication, Document De Travail Année : 2025

Brochette first-passage percolation

Résumé

We investigate a novel first-passage percolation model, referred to as the Brochette first-passage percolation model, where the passage times associated with edges lying on the same line are equal. First, we establish a point-to-point convergence theorem, identifying the time constant. In particular, we explore the case where the time constant vanishes and demonstrate the existence of a wide range of possible behaviours. Next, we prove a shape theorem, showing that the limiting shape is the $L^1$ diamond. Finally, we extend the analysis by proving a point-to-point convergence theorem in the setting where passage times are allowed to be infinite.
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Dates et versions

hal-04896984 , version 1 (20-01-2025)

Identifiants

  • HAL Id : hal-04896984 , version 1

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Maxime Marivain. Brochette first-passage percolation. 2025. ⟨hal-04896984⟩
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