43 citations · 74 across the 9 of their papers we have counts for
9 papers
The process of fluctuations of the giant component of an Erdős-Rényi graph
Nathanaël Enriquez, Gabriel Faraud, Sophie Lemaire
We present a detailed study of the evolution of the giant component of the Erdős-Rényi graph process as the mean degree increases from 1 to infinity. It leads to the identification…
Long induced paths in a configuration model
Nathanaël Enriquez, Gabriel Faraud, Laurent Ménard +1
In an article published in 1987 in Combinatorica \cite{MR918397}, Frieze and Jackson established a lower bound on the length of the longest induced path (and cycle) in a sparse ran…
Depth First Exploration of a Configuration Model
Nathanaël Enriquez, Gabriel Faraud, Laurent Ménard +1
We introduce an algorithm that constructs a random uniform graph with prescribed degree sequence together with a depth first exploration of it. In the so-called supercritical regim…
Limiting shape of the Depth First Search tree in an Erdős-Rényi graph
Nathanaël Enriquez, Gabriel Faraud, Laurent Ménard
We show that the profile of the tree constructed by the Depth First Search Algorithm in the giant component of an Erdős-Rényi graph with vertices and connection probability $c/…
Connection times in large ad-hoc mobile networks
Hanna Döring, Gabriel Faraud, Wolfgang König
We study connectivity properties in a probabilistic model for a large mobile ad-hoc network. We consider a large number of participants of the system moving randomly, independently…
Bessel bridges decomposition with varying dimension. Applications to finance
Gabriel Faraud, Stéphane Goutte
We consider a class of stochastic processes containing the classical and well-studied class of Squared Bessel processes. Our model, however, allows the dimension be a function of t…
Almost sure convergence for stochastically biased random walks on trees
Gabriel Faraud, Yueyun Hu, Zhan Shi
We are interested in the biased random walk on a supercritical Galton--Watson tree in the sense of Lyons, Pemantle and Peres, and study a phenomenon of slow movement. In order to o…
Estimates on the speedup and slowdown for a diffusion in a drifted brownian potential
Gabriel Faraud
We study a model of diffusion in a brownian potential. This model was firstly introduced by T. Brox (1986) as a continuous time analogue of random walk in random environment. We es…
A central limit theorem for random walk in random environment on marked Galton-Watson trees
Gabriel Faraud
In this article we focus on a general model of random walk on random marked trees. We prove a recurrence criterion, analogue to the recurrence criterion proved by R. Lyons and Robi…