Long-time tails in the parabolic Anderson model with bounded potential

Marek Biskup, Wolfgang Koenig

We consider the parabolic Anderson problem ${\partial }_{t}u=\kappa \Delta u+\xi u$ on $(0,\infty )\times {\mathbb{Z}}^d$ with random i.i.d. potential $\xi =(\xi (z){)}_{z\in {\mathbb{Z}}^d}$ and the initial condition $u(0,\cdot)…