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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 (fromto)  21982263 
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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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