Scaling property of flux fluctuations from random walks

We study dynamical scaling of flux fluctuation σ̄ (t) from the one-random-walker model on regular lattices and complex networks and compare it to the surface width W (t) of a corresponding growth model. On the regular lattices, we analytically show that σ̄ (t) undergoes a crossover from the nontrivial scaling regime to the trivial one by increasing time t, and we verify the results by numerical simulations. In contrast to the results on the regular lattices, σ̄ (t) does not show any crossover behavior on complex networks and satisfies the scaling relation σ̄ (t) ∼ t1/2 for any t. On the other hand, we show that W (t) of the corresponding model on complex networks has two different scaling regimes, W∼ t1/2 for t/N and W (t) ∼t for t/N.