Geometric characterization of intermittency in the parabolic Anderson model

Jürgen Gärtner, Wolfgang König, Stanislav Molchanov

We consider the parabolic Anderson problem ${\partial }_{t}u=\Delta u+\xi (x)u$ on ${\mathbb{R}}_{+}\times {\mathbb{Z}}^d$ with localized initial condition $u(0,x)={\delta }_0(x)$ and random i.i.d. potential $…