Brochette first-passage percolation
Abstract
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 upper L Superscript 1 L 1 $L^1$ 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.
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Publication details
- Journal / source
- Journal of Applied Probability
- Volume
- 63
- Issue
- 3
- Pages
- 1281–1301
- Publication date
- 14 April 2026
- Language
- EN