9 papers
Local limits of conditioned marked Galton Watson trees
Romain Abraham, Sonia Boulal, Pierre Debs
We consider a Galton-Watson tree where each node is marked independently of each others with a probability depending on its outdegree. We give a complete picture of the local conve…
Sub-diffusive behavior of a recurrent Axis-Driven Random Walk
Pierre Andreoletti, Pierre Debs
We study the second order of the number of excursions of a simple random walk with a bias that drives a return toward the origin along the axes introduced by P. Andreoletti and P.…
Simple random walk on Z^2 perturbed on the axis (renewal case)
Pierre Andreoletti, Pierre Debs
We study a simple random walk on Z^2 with constraints on the axis. Motivation comes from physics when particles (a gas for example, see [Dal88]) are submitted to a local field. In…
Power of the Crowd
Athanasios Batakis, Pierre Debs, Dorian Le Peutrec
Consider an Galton Watson tree of height : each leaf has one of opinions or not. In other words, for , at generation thinks with probabil…
Penalization of Galton-Watson processes
Romain Abraham, Pierre Debs
We apply the penalization technique introduced by Roynette, Vallois, Yor for Brownian motion to Galton-Watson processes with a penalizing function of the form where P is…
Diseases transmission in a z-ary tree
Pierre Debs, Thomas Haberkorn
We extend some results of Itai Benjamini and Yuri Lima (see \href{http://arxiv.org/pdf/1305.2610.pdf}{\cite{Benjamini}}). In this paper they consider a binary tree of…
Spread of visited sites of a random walk along the generations of a branching process
Pierre Andreoletti, Pierre Debs
In this paper we consider a null recurrent random walk in random environment on a super-critical Galton-Watson tree. We consider the case where the log-Laplace transform of the…
The number of generations entirely visited for recurrent random walks on random environment
Pierre Andreoletti, Pierre Debs
In this paper we are interested in a random walk in a random environment on a super-critical Galton-Watson tree. We focus on the recurrent cases already studied by Y. Hu and Z. Shi…
Penalisation of the symmetric random walk by several functions of the supremum
Pierre Debs
In this paper, we penalised the standard random walk by several functions of its maximum. The aim is to show that in spite of very close penalisation functions, under the new proba…