Random walk and Pair-Annihilation Processes on Scale-Free Networks
  We investigate the dynamic scaling properties of stochastic particle systems on a non-deterministic scale-free network. It has been known that the dynamic scaling behavior depends on the degree distribution exponent of the underlying scale-free network. Our study shows that it also depends on the global structure of the underlying network. In random walks on the tree structure scale-free network, we find that the relaxation time follows a power-law scaling $\tau\sim N$ with the network size $N$. And the random walker return probability decays algebraically with the decay exponent which varies from node to node. On the other hand, in random walks on the looped scale-free network, they do not show the power-law scaling. We also study a pair-annihilation process on the scale-free network with the tree and the looped structure, respectively. We find that the particle density decays algebraically in time both cases, but with the different exponent. 
Jae Dong Noh and Sang-Woo Kim