Projects per year

### Abstract

We consider a branching random walk on the lattice, where the

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.

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 |

### Keywords

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

## Fingerprint Dive into the research topics of 'Intermittency for branching random walk in Pareto environment'. Together they form a unique fingerprint.

## Projects

- 1 Finished

### EPSRC Posdoctoral Fellowship in Applied Probability for Dr Matthew I Roberts

Engineering and Physical Sciences Research Council

3/04/13 → 2/07/16

Project: Research council

## Profiles

### Matthew Roberts

- Department of Mathematical Sciences - Royal Society University Research Fellow & Reader
- EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
- Probability Laboratory at Bath

Person: Research & Teaching