Julien Verges

collaborators

3 papers

math.PR2025

Concentration inequalities and large deviations for continuous greedy animals and paths

Julien Verges

Consider the continuous greedy paths model: given a $d$ -dimensional Poisson point process with positive marks interpreted as masses, let $P (ℓ)$ denote the maximum mass g…

math.PR2024

Large deviation principle at speed $n$ for the random metric in first-passage percolation

Julien Verges

Consider standard first-passage percolation on $Z^{d}$ . We study the lower-tail large deviations of the rescaled random metric $T_{n}$ restricted to a box. If…

math.PR2024

Law of large numbers for greedy animals and paths in a Poissonian environment

Julien Verges

We study two continuous and isotropic analogues of the model of greedy lattice animals introduced by Cox, Gandolfi, Griffin and Kesten in 1993. In our framework, animals collect ma…

Concentration inequalities and large deviations for continuous greedy animals and paths

Large deviation principle at speed n for the random metric in first-passage percolation

Law of large numbers for greedy animals and paths in a Poissonian environment

Large deviation principle at speed $n$ for the random metric in first-passage percolation