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 an ergodic environment

Julien Verges

Consider a family of random masses $m (v)$ indexed by vertices of the lattice $Z^{d}$ . In the case where the masses are i.i.d.\ and satisfy a certain moment condition…

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 an ergodic environment

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