Flux fluctuations in a multi-random-walker model and surface growth   dynamics
  We study the dynamics of visitation flux in a multi-random-walker model by comparison to surface growth dynamics in which one random walker drops a particle to a node at each time the walker visits the node. In each independent experiment (trial or day) for the multi-random-walker model, the number of walkers are randomly chosen from the uniform distribution $[< N_{RW} > -\triangle N_{RW}, < N_{RW} > +\triangle N_{RW} ]$. The averaged fluctuation $\bar {\sigma} ({T_{RW}})$ of the visitations over all nodes $i$ and independent experiments is shown to satisfy the power-law dependence on the walk step $T_{RW}$ as $\bar {\sigma} ({T_{RW}})\simeq {T_{RW}}^\beta$. Furthermore two distinct values of the exponent $\beta$ are found on a scale-free network, a random network and regular lattices. One is $\beta_i$, which is equal to the growth exponent $\beta$ for the surface fluctuation $W$ in one-random-walker model, and the other is $\beta=1$. $\beta_i$ is found for small $\triangle N_{RW}$ or for the system governed by the internal intrinsic dynamics. In contrast $\beta=1$ is found for large $\triangle N_{RW}$ or for the system governed by the external flux variations. The implications of our results to the recent studies on fluctuation dynamics of the nodes on networks are discussed. 
S. Y. Yoon, Byoung-sun Ahn, Yup Kim