### Abstract

Using a high performance computer cluster, we run simulations regarding an open problem about d-dimensional critical branching random walks in a random IID environment The environment is given by the rule that at every site independently, with probability p ∈ [0;1], there is a cookie, completely suppressing the branching of any particle located there. The simulations suggest self averaging: the asymptotic survival probability in n steps is the same in the annealed and the quenched case; it is 2/qn, where q: = 1 - p. This particular asymptotics indicates a non-trivial phenomenon: the tail of the survival probability (both in the annealed and the quenched case) is the same as in the case of non-spatial unit time critical branching, where the branching rule is modified: branching only takes place with probability q for every particle at every iteration.

Original language | English (US) |
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Pages (from-to) | 169-193 |

Number of pages | 25 |

Journal | Monte Carlo Methods and Applications |

Volume | 17 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1 2011 |

### Keywords

- Branching random walk
- Catalytic branching
- Critical branching
- Mild obstacles
- Random environment
- Simulation

### ASJC Scopus subject areas

- Statistics and Probability
- Applied Mathematics

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## Cite this

*Monte Carlo Methods and Applications*,

*17*(2), 169-193. https://doi.org/10.1515/MCMA.2011.008