The integrated density of states of the random graph Laplacian

Aspelmeier, Timo; Zippelius, Annette

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The integrated density of states of the random graph Laplacian

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Aspelmeier, Timo
Fellow Group Polymers, complex fluids and disordered systems, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;
Research Group of Statistical Inverse-Problems in Biophysics, MPI for Biophysical Chemistry, Max Planck Society;

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Zippelius, Annette
Fellow Group Polymers, complex fluids and disordered systems, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Aspelmeier, T., & Zippelius, A. (n.d.). The integrated density of states of the random graph Laplacian. Statistical Physics, 144, 759-773. Retrieved from http://arxiv.org/abs/1008.1087.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-17E6-2

Abstract

We analyse the density of states of the random graph Laplacian in the percolating regime. A symmetry argument and knowledge of the density of states in the nonpercolating regime allows us to isolate the density of states of the percolating cluster (DSPC) alone, thereby eliminating trivially localised states due to finite subgraphs. We derive a nonlinear integral equation for the integrated DSPC and solve it with a population dynamics algorithm. We discuss the possible existence of a mobility edge and give strong evidence for the existence of discrete eigenvalues in the whole range of the spectrum.