Intermittency for branching random walk in Pareto environment

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.