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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 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.
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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Dive into the research topics of 'One-point localization for branching random walk in Pareto environment'. Together they form a unique fingerprint.Projects
- 1 Finished
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EPSRC Posdoctoral Fellowship in Applied Probability for Dr Matthew I Roberts
Roberts, M. (PI)
Engineering and Physical Sciences Research Council
3/04/13 → 2/07/16
Project: Research council