Fractal Weyl law for Linux Kernel Architecture

Abstract

We study the properties of spectrum and eigenstates of the Google matrix of a directed network formed by the procedure calls in the Linux Kernel. Our results obtained for various versions of the Linux Kernel show that the spectrum is characterized by the fractal Weyl law established recently for systems of quantum chaotic scattering and the Perron-Frobenius operators of dynamical maps. The fractal Weyl exponent is found to be $\nu \approx 0.63$ that corresponds to the fractal dimension of the network $d\approx 1.2$. The eigenmodes of the Google matrix of Linux Kernel are localized on certain principal nodes. We argue that the fractal Weyl law should be generic for directed networks with the fractal dimension $d<2$.

RevTex 6 pages, 7 figs, linked to arXiv:1003.5455[cs.SE]. Research at http://www.quantware.ups-tlse.fr/, Improved version, changed format

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• Anderson Transitions
• Fractality in complex networks: critical and supercritical skeletons
• Fractal Weyl laws for chaotic open systems
• Quantum-to-classical crossover of quasi-bound states in open quantum systems
• Semiclassical structure of chaotic resonance eigenfunctions
• Fractal Weyl law for quantum fractal eigenstates
• Spectral properties of the Google matrix of the World Wide Web and other directed networks
• Delocalization transition for the Google matrix
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