### Abstract

branching rates are given by an i.i.d. Pareto random potential. We

describe the process, including a detailed shape theorem, in terms

of a system of growing lilypads. As an application we show that the

branching random walk is intermittent, in the sense that most particles

are concentrated on one very small island with large potential.

Moreover, we compare the branching random walk to the parabolic

Anderson model and observe that although the two systems show

similarities, the mechanisms that control the growth are fundamentally

different.

Original language | English |
---|---|

Pages (from-to) | 2198-2263 |

Number of pages | 66 |

Journal | Annals of Probability |

Volume | 44 |

Issue number | 3 |

Early online date | 16 May 2016 |

DOIs | |

Publication status | Published - 31 May 2016 |

### Fingerprint

### Keywords

- Branching random walk
- random environment
- Parabolic Anderson model
- Intermittency

### Cite this

**Intermittency for branching random walk in Pareto environment.** / Ortgiese, Marcel; Roberts, Matthew I.

Research output: Contribution to journal › Article

*Annals of Probability*, vol. 44, no. 3, pp. 2198-2263. https://doi.org/10.1214/15-AOP1021

}

TY - JOUR

T1 - Intermittency for branching random walk in Pareto environment

AU - Ortgiese, Marcel

AU - Roberts, Matthew I.

PY - 2016/5/31

Y1 - 2016/5/31

N2 - We consider a branching random walk on the lattice, where thebranching rates are given by an i.i.d. Pareto random potential. Wedescribe the process, including a detailed shape theorem, in termsof a system of growing lilypads. As an application we show that thebranching random walk is intermittent, in the sense that most particlesare concentrated on one very small island with large potential.Moreover, we compare the branching random walk to the parabolicAnderson model and observe that although the two systems showsimilarities, the mechanisms that control the growth are fundamentallydifferent.

AB - We consider a branching random walk on the lattice, where thebranching rates are given by an i.i.d. Pareto random potential. Wedescribe the process, including a detailed shape theorem, in termsof a system of growing lilypads. As an application we show that thebranching random walk is intermittent, in the sense that most particlesare concentrated on one very small island with large potential.Moreover, we compare the branching random walk to the parabolicAnderson model and observe that although the two systems showsimilarities, the mechanisms that control the growth are fundamentallydifferent.

KW - Branching random walk

KW - random environment

KW - Parabolic Anderson model

KW - Intermittency

U2 - 10.1214/15-AOP1021

DO - 10.1214/15-AOP1021

M3 - Article

VL - 44

SP - 2198

EP - 2263

JO - Annals of Probability

JF - Annals of Probability

SN - 0091-1798

IS - 3

ER -