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Localization for branching random walks in random environment

Author

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  • Hu, Yueyun
  • Yoshida, Nobuo

Abstract

We consider branching random walks in d-dimensional integer lattice with time-space i.i.d. offspring distributions. This model is known to exhibit a phase transition: If d>=3 and the environment is "not too random", then, the total population grows as fast as its expectation with strictly positive probability. If, on the other hand, d

Suggested Citation

  • Hu, Yueyun & Yoshida, Nobuo, 2009. "Localization for branching random walks in random environment," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1632-1651, May.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:5:p:1632-1651
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    Cited by:

    1. Gao, Zhiqiang & Liu, Quansheng, 2016. "Exact convergence rates in central limit theorems for a branching random walk with a random environment in time," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2634-2664.
    2. Mallein, Bastien & Miłoś, Piotr, 2019. "Maximal displacement of a supercritical branching random walk in a time-inhomogeneous random environment," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3239-3260.
    3. Francis Comets & Nobuo Yoshida, 2011. "Branching Random Walks in Space–Time Random Environment: Survival Probability, Global and Local Growth Rates," Journal of Theoretical Probability, Springer, vol. 24(3), pages 657-687, September.

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