Codice  QDD 156 
Titolo  Rumor processes in random environment on N and on GaltonWatson trees 
Data  20130531 
Autore/i  BERTACCHI, D.; ZUCCA, F. 
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Abstract  The aim of this paper is to study rumor processes in random environment. In a rumor
process a signal starts from the stations of a fixed vertex (the root) and travels on a graph from
vertex to vertex. We consider two rumor processes. In the rework process each station, when
reached by the signal, transmits it up to a random distance. In the reverse rework process, on the
other hand, stations do not send any signal but they listen for it up to a random distance. The
first random environment that we consider is the deterministic 1dimensional tree N with a random
number of stations on each vertex; in this case the root is the origin of N. We give conditions for
the survival/extinction on almost every realization of the sequence of stations. Later on, we study
the processes on GaltonWatson trees with random number of stations on each vertex. We show
that if the probability of survival is positive, then there is survival on almost every realization of
the infinite tree such that there is at least one station at the root. We characterize the survival of
the process in some cases and we give sufficient conditions for survival/extinction. 
