Survival of Branching Random Walks in Random Environment
نویسندگان
چکیده
منابع مشابه
Survival of branching random walks in random environment
We study survival of nearest-neighbour branching random walks in random environment (BRWRE) on Z. A priori there are three different regimes of survival: global survival, local survival, and strong local survival. We show that local and strong local survival regimes coincide for BRWRE and that they can be characterized with the spectral radius of the first moment matrix of the process. These re...
متن کاملOn multidimensional branching random walks in random environment
We study branching random walks in random i.i.d. environment in Zd, d ≥ 1. For this model, the population size cannot decrease, and a natural definition of recurrence is introduced. We prove a dichotomy for recurrence/transience, depending only on the support of the environmental law. We give sufficient conditions for recurrence and for transience. In the recurrent case, we study the asymptotic...
متن کاملBranching random walks in random environment on Cayley graphs
We review some recent results concerning recurrence and transience for branching random walks in random environment on ddimensional lattices and on trees. We obtain some generalizations of these results for the case when the branching random walk in random environment takes place on arbitrary infinite connected Cayley graph.
متن کاملCentral Limit Theorem for Branching Random Walks in Random Environment
We consider branching random walks in d-dimensional integer lattice with time-space i.i.d. offspring distributions. When d ≥ 3 and the fluctuation of the environment is well moderated by the random walk, we prove a central limit theorem for the density of the population, together with upper bounds for the density of the most populated site and the replica overlap. We also discuss the phase tran...
متن کاملBranching Random Walks in Space-Time Random Environment: Survival Probability, Global and Local Growth Rates
We study the survival probability and the growth rate for branching random walks in random environment (BRWRE). The particles perform simple symmetric random walks on the d-dimensional integer lattice, while at each time unit, they split into independent copies according to time-space i.i.d. offspring distributions. The BRWRE is naturally associated with the directed polymers in random environm...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Theoretical Probability
سال: 2009
ISSN: 0894-9840,1572-9230
DOI: 10.1007/s10959-009-0227-5