Branching Random Walks and Interacting particle System in Random Environment.

Abstract

The first objective of this research project is to study the extinction probability and the main properties of critical parameters associated with branching random walks. We study these properties by means of an infinite dimensional generating function. In this project we address the following issues: (1) characterization of the set of fixed points (extinction probabilities) of the generating function of an irreducible branching random walks on discrete time and, (2) characterization of the global survival critical parameter for branching random walks in continuous time. We intend also to study the diffusion of an information in random graphs given by the cluster of percolation of independent site percolation model by means of suitable couplings with a branching random walk in order to prove survival or extinction of the information.