3 papers
math.PR2026
Rate of convergence of the conditioned random walk towards the Brownian bridge
Laurent Decreusefond, Antonin Jacquet
We study the rate of convergence of two discrete processes towards the Brownian bridge: the random walk conditioned to be zero at time 2n and the empirical process which appears in…
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…