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Spectral Asymptotics of Percolation Hamiltonians on Amenable Cayley Graphs

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Methods of Spectral Analysis in Mathematical Physics

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 186))

Abstract

In this paper we study spectral properties of adjacency and Laplace operators on percolation subgraphs of Cayley graphs of amenable, finitely generated groups. In particular we describe the asymptotic behaviour of the integrated density of states (spectral distribution function) of these random Hamiltonians near the spectral minimum.

The first part of the note discusses various aspects of the quantum percolation model, subsequently we formulate a series of new results, and finally we outline the strategy used to prove our main theorem.

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Authors and Affiliations

  1. Emmy-Noether-Programme of the Deutsche Forschungsgemeinschaft & Fakultät für Mathematik, 09107 TU, Chemnitz, Germany

    Tonći Autunović & Ivan Veselić

Authors
  1. Tonći Autunović
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  2. Ivan Veselić
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Editor information

Editors and Affiliations

  1. Institut of Mathematics, Polish Academy of Sciences, ul. Sw. Tomasza 30/7, 31-027, Krakow, Poland

    Jan Janas

  2. Department of Mathematics, Lund Institute of Technology, 221 00, Lund, Sweden

    Pavel Kurasov

  3. Department of Mathematical Physics, St. Petersburg State University, Ulyanovskaya 1, 198904, St. Petersburg, Russia

    Sergei Naboko

  4. Department of Mathematics South Kensington Campus, Imperial College London, SW7 2AZ, London, UK

    Ari Laptev

  5. Department of Mathematics, Royal Institute of Technology, 100 44, Stockholm, Sweden

    Ari Laptev

  6. Department of Mathematics, University of Alabama, 452 Campbell Hall, Birmingham, AL, 35294-1170, USA

    Günter Stolz

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© 2008 Birkhäuser Verlag Basel/Switzerland

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Autunović, T., Veselić, I. (2008). Spectral Asymptotics of Percolation Hamiltonians on Amenable Cayley Graphs. In: Janas, J., Kurasov, P., Naboko, S., Laptev, A., Stolz, G. (eds) Methods of Spectral Analysis in Mathematical Physics. Operator Theory: Advances and Applications, vol 186. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8755-6_1

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