Random walk and trapping processes on scale-free networks

Details Random walk and trapping processes on scale-free networks Random walk and trapping processes on scale-free networks

2004-06-17

arxiv.org/abs/cond-mat/0406388v1

Phys. Rev. E, 70, 046116 (2004).

Physics

Condensed Matter

Disordered Systems and Neural Networks

8 pages, 5 figures

Scientific paper

10.1103/PhysRevE.70.046116

In this work we investigate the dynamics of random walk processes on scale-free networks in a short to moderate time scale. We 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. We show 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 we 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 our 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.

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