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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
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
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Dive into the research topics of 'Intermittency 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
Profiles
-
Matt Roberts
- Department of Mathematical Sciences - Royal Society University Research Fellow
- EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
- Probability Laboratory at Bath
Person: Research & Teaching