3 papers
math.PR2025
Strict inequality between the time constants of first-passage percolation and directed first-passage percolation
Antonin Jacquet
In the models of first-passage percolation and directed first-passage percolation on , we consider a family of i.i.d. random variables indexed by the set of edges of…
math.PR2024
Disjoint finite geodesics in first-passage percolation
Olivier Durieu, Jean-Baptiste Gouéré, Antonin Jacquet
We investigate first-passage percolation on the lattice for dimensions . Each edge of the graph is assigned an independent copy of a non-negative random variab…
math.PR2023
Geodesics cross any pattern in first-passage percolation without any moment assumption and with possibly infinite passage times
Antonin Jacquet
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…