On explosions in heavy-tailed branching random walks

@article{Amini2013OnEI,
  title={On explosions in heavy-tailed branching random walks},
  author={O. Amini and L. Devroye and S. Griffiths and Neil Olver},
  journal={Annals of Probability},
  year={2013},
  volume={41},
  pages={1864-1899}
}
  • O. Amini, L. Devroye, +1 author Neil Olver
  • Published 2013
  • Mathematics
  • Annals of Probability
  • Consider a branching random walk on R, with offspring distribution Z and nonnegative displacement distribution W. We say that explosion occurs if an infinite number of particles may be found within a finite distance of the origin. In this paper, we investigate this phenomenon when the offspring distribution Z is heavy-tailed. Under an appropriate condition, we are able to characterize the pairs (Z,W) for which explosion occurs, by demonstrating the equivalence of explosion with a seemingly much… CONTINUE READING

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