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Dynamical Scaling Behavior of Percolation Clusters in Scale-free Networks | | F. Jasch
; C. von Ferber
; A. Blumen
; | | Date: |
25 Feb 2004 | | Subject: | Statistical Mechanics | cond-mat.stat-mech | | Affiliation: | Freiburg | | Abstract: | In this work we investigate the spectra of Laplacian matrices that determine many dynamic properties of scale-free networks below and at the percolation threshold. We use a replica formalism to develop analytically, based on an integral equation, a systematic way to determine the ensemble averaged eigenvalue spectrum for a general type of tree-like networks. Close to the percolation threshold we find characteristic scaling functions for the density of states rho(lambda) of scale-free networks. rho(lambda) shows characteristic power laws rho(lambda) ~ lambda^alpha_1 or rho(lambda) ~ lambda^alpha_2 for small lambda, where alpha_1 holds below and alpha_2 at the percolation threshold. In the range where the spectra are accessible from a numerical diagonalization procedure the two methods lead to very similar results. | | Source: | arXiv, cond-mat/0402622 | | Other source: | [GID 749830] pmid15324134 | | Services: | Forum | Review | PDF | Favorites | |
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