### Abstract

Original language | English |
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Article number | 6 |

Number of pages | 20 |

Journal | Electronic Journal of Probability |

Volume | 22 |

DOIs | |

Publication status | Published - 17 Jan 2017 |

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**One-point localization for branching random walk in Pareto environment.** / Ortgiese, Marcel; Roberts, Matthew.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - One-point localization for branching random walk in Pareto environment

AU - Ortgiese, Marcel

AU - Roberts, Matthew

PY - 2017/1/17

Y1 - 2017/1/17

N2 - We consider a branching random walk on the lattice, where the branching rates are given by an i.i.d. Pareto random potential. We show a very strong form of intermittency, where with high probability most of the mass of the system is concentrated in a single site with high potential. The analogous one-point localization is already known for the parabolic Anderson model, which describes the expected number of particles in the same system. In our case, we rely on very fine estimates for the behaviour of particles near a good point. This complements our earlier results that in the rescaled picture most of the mass is concentrated on a small island.

AB - We consider a branching random walk on the lattice, where the branching rates are given by an i.i.d. Pareto random potential. We show a very strong form of intermittency, where with high probability most of the mass of the system is concentrated in a single site with high potential. The analogous one-point localization is already known for the parabolic Anderson model, which describes the expected number of particles in the same system. In our case, we rely on very fine estimates for the behaviour of particles near a good point. This complements our earlier results that in the rescaled picture most of the mass is concentrated on a small island.

UR - https://doi.org/10.1214/16-EJP22

U2 - 10.1214/16-EJP22

DO - 10.1214/16-EJP22

M3 - Article

VL - 22

JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

SN - 1083-6489

M1 - 6

ER -