5 papers · 1 filter
Concentration inequalities and large deviations for continuous greedy animals and paths
Julien Verges
Consider the continuous greedy paths model: given a -dimensional Poisson point process with positive marks interpreted as masses, let denote the maximum mass g…
Large deviation principle at speed for the random metric in first-passage percolation
Julien Verges
Consider standard first-passage percolation on . We study the lower-tail large deviations of the rescaled random metric restricted to a box. If…
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…
Law of large numbers for greedy animals and paths in an ergodic environment
Julien Verges
Consider a family of random masses indexed by vertices of the lattice . In the case where the masses are i.i.d.\ and satisfy a certain moment condition…
Large deviation principle at speed for the random metric in first-passage percolation
Julien Verges
We consider the standard first passage percolation model on with bounded and bounded away from zero weights. We show that the rescaled passage time $\widetilde{\mathb…