Strong Local Survival of Branching Random Walks is Not Monotone
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...
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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...
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In recent years several authors have obtained limit theorems for Ln, the location of the rightmost particle in a supercritical branching random walk but all of these results have been proved under the assumption that the offspring distribution has (p(O)=.fexp(Ox)dF(x)0. In this paper we investigate what happens when there is a slowly varying function K so that 1-F(x)~x-qK(x) as x...
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ژورنال
عنوان ژورنال: Advances in Applied Probability
سال: 2014
ISSN: 0001-8678,1475-6064
DOI: 10.1239/aap/1401369700