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Random Walks, Boundaries and Spectra pp 235–258Cite as

Percolation Hamiltonians

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Part of the book series: Progress in Probability ((PRPR,volume 64))

Abstract

There has been quite some activity and progress concerning spectral asymptotics of random operators that are defined on percolation subgraphs of different types of graphs. In this short survey we record some of these results and explain the necessary background coming from different areas in mathematics: graph theory, group theory, probability theory and random operators.

Mathematics Subject Classification (2000). Primary 05C25; Secondary 82B43.

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Author information

Authors and Affiliations

  1. Mathematisches Institut der Universität München, Theresienstr. 39, D-80333, München, Germany

    Peter Müller

  2. Fakultät für Mathematik, TU-Chemnitz, D-09107, Chemnitz, Germany

    Peter Stollmann

Authors
  1. Peter Müller
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  2. Peter Stollmann
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Correspondence to Peter Müller .

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Editors and Affiliations

  1. Mathematisches Inst., Universität Jena, Ernst-Abbe-Platz 2, Jena, 07737, Germany

    Daniel Lenz

  2. Inst. Mathematik C, TU Graz, Steyrergasse 30, Graz, 8010, Austria

    Florian Sobieczky

  3. Inst. Mathematik C, TU Graz, Steyrergasse 30, Graz, 8010, Austria

    Wolfgang Woess

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Müller, P., Stollmann, P. (2011). Percolation Hamiltonians. In: Lenz, D., Sobieczky, F., Woess, W. (eds) Random Walks, Boundaries and Spectra. Progress in Probability, vol 64. Springer, Basel. https://doi.org/10.1007/978-3-0346-0244-0_13

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