Analytical results for random walks in the presence of disorder and traps

In this paper, we study the dynamics of a random walker diffusing on a disordered one-dimensional lattice with random trappings. The distribution of escape probabilities is computed exactly for any strength of the disorder. These probabilities do not display any multifractal properties contrary to previous numerical claims. The explanation for this apparent multifractal behavior is given, and our conclusion are supported by numerical calculations. These exact results are exploited to compute the large time asymptotics of the survival probability (or the density) which is found to decay as $\exp [-Ct^{1/3}\log^{2/3}(t)]$. An exact lower bound for the density is found to decay in a similar way.