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- W2024900738 abstract "We compare two models of a continuous-time branching random walk on the multidimensional lattice Z d (d ≥ 1) in random environments. In the first of these models, the branching medium formed of birth-and-death processes at every lattice site is assumed to be spatially homogeneous. In the second model, the branching medium containing a single source of branching located at the origin is spatially non homogeneous. The underlying random walk is assumed to be symmetric in both models. We study the long-time behavior of the moments (p ≥ 1) for the local particle population and the total one, obtained by averaging over the medium realizations. Assumptions making the long-time behavior of the moments to coincide for the number of particles at an arbitrary site of the lattice and that on the whole lattice, are obtained. It is shown that these assumptions hold for random potentials having Weibull-type and Gumbel-type upper tails. Our results are useful for experimental design in the framework of these models." @default.
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- W2024900738 date "2012-08-01" @default.
- W2024900738 modified "2023-10-02" @default.
- W2024900738 title "Symmetric Branching Walks in Homogeneous and Non Homogeneous Random Environments" @default.
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- W2024900738 doi "https://doi.org/10.1080/03610918.2012.625856" @default.
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