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  The integrated density of states of the random graph Laplacian.

Aspelmeier, T., & Zippelius, A. (2011). The integrated density of states of the random graph Laplacian. Journal of Statistical Physics, 144, 759-773. doi:10.1007/s10955-011-0271-2.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-002B-85F1-B Version Permalink: http://hdl.handle.net/11858/00-001M-0000-002B-85F4-5
Genre: Journal Article

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Aspelmeier, T.1, Author              
Zippelius, A.2, Author              
Affiliations:
1Research Group of Statistical Inverse-Problems in Biophysics, MPI for Biophysical Chemistry, Max Planck Society, ou_1113580              
2Fellow Group Polymers, complex fluids and disordered systems, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_2063298              

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 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.

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Language(s): eng - English
 Dates: 2011-07-292011-08
 Publication Status: Published in print
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 Rev. Method: Peer
 Identifiers: DOI: 10.1007/s10955-011-0271-2
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Title: Journal of Statistical Physics
Source Genre: Journal
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Pages: - Volume / Issue: 144 Sequence Number: - Start / End Page: 759 - 773 Identifier: -