Competition between surface relaxation and ballistic deposition models in scale free networks

In this paper we study the scaling behavior of the fluctuations in the steady state $W_S$ with the system size $N$ for a surface growth process given by the competition between the surface relaxation (SRM) and the Ballistic Deposition (BD) models on degree uncorrelated Scale Free networks (SF), characterized by a degree distribution $P(k)\sim k^{-\lambda}$, where $k$ is the degree of a node. It is known that the fluctuations of the SRM model above the critical dimension ($d_c=2$) scales logarithmically with $N$ on euclidean lattices. However, Pastore y Piontti {\it et. al.} [A. L. Pastore y Piontti {\it et. al.}, Phys. Rev. E {\bf 76}, 046117 (2007)] found that the fluctuations of the SRM model in SF networks scale logarithmically with $N$ for $\lambda
Comment: 8 pages, 6 figures