Julien Verges

most citedLarge deviation principle at speed

n^{d}

for the random metric in first-passage percolation

1 citations · 1 across the 3 of their papers we have counts for

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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…

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…

math.PR2024★ 1 cited

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

Julien Verges

We consider the standard first passage percolation model on $Z^{d}$ with bounded and bounded away from zero weights. We show that the rescaled passage time $\widetilde{\mathb…

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

Law of large numbers for greedy animals and paths in an ergodic environment

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

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

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