Random walk and trapping processes on scale-free networks

In this work I investigate the dynamics of random walk processes on scale-free networks in a short to moderate time scale. I perform extensive simulations for the calculation of the mean squared displacement, the network coverage, and the survival probability on a network with a concentration $c$ of static traps. It is shown that the random walkers remain close to their origin, but cover a large part of the network at the same time. This behavior is markedly different than usual random walk processes in the literature. For the trapping problem I numerically compute $\Phi (n,c)$, the survival probability of mobile species at time $n$, as a function of the concentration of trap nodes, $c$. Comparison of these results to the Rosenstock approximation indicate that this is an adequate description for networks with $2<\gamma <3$ and yield an exponential decay. For $\gamma >3$ the behavior is more complicated and one needs to employ a truncated cumulant expansion.