Mass concentration and aging in the parabolic Anderson model with doubly-exponential tails

Marek Biskup, Wolfgang Koenig, Renato Soares dos Santos

We study the solutions $u=u(x,t)$ to the Cauchy problem on ${\mathbb{Z}}^d\times (0,\infty )$ for the parabolic equation ${\partial }_{t}u=\Delta u+\xi u$ with initial data $u(x,0)=1_{\{0\}}(x)$. He…