Brochette first-passage percolation

2025/01/20 by Marivain, Maxime
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2501.11398

Abstract

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 L¹ 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.

Related

• Weak shape theorem in first passage percolation with infinite passage times
• Monotonicity in first-passage percolation
• Covering monotonicity of the limit shapes of first passage percolation on crystal lattices
• A Central Limit Theorem for First Passage Percolation in the Slab
• A Central Limit Theorem for First Passage Percolation in the Slab