Spectral properties of the Laplacian on bond-percolation graphs

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dc.creatorKirsch, Werner
dc.creatorMüller, Peter
dc.date2004-07-21
dc.date2005-12-13
dc.date.accessioned2026-07-07T07:40:54Z
dc.date.available2026-07-07T07:40:54Z
dc.descriptionBond-percolation graphs are random subgraphs of the d-dimensional integer lattice generated by a standard bond-percolation process. The associated graph Laplacians, subject to Dirichlet or Neumann conditions at cluster boundaries, represent bounded, self-adjoint, ergodic random operators with off-diagonal disorder. They possess almost surely the non-random spectrum [0,4d] and a self-averaging integrated density of states. The integrated density of states is shown to exhibit Lifshits tails at both spectral edges in the non-percolating phase. While the characteristic exponent of the Lifshits tail for the Dirichlet (Neumann) Laplacian at the lower (upper) spectral edge equals d/2, and thus depends on the spatial dimension, this is not the case at the upper (lower) spectral edge, where the exponent equals 1/2.
dc.description19 pages; presentation slightly improved, some comments and references added; to appear in Mathematische Zeitschrift
dc.identifierhttps://arxiv.org/abs/math-ph/0407047
dc.identifierhttp://arxiv.org/abs/math-ph/0407047
dc.identifierMath. Z. 252 (2006) 899 - 916
dc.identifierdoi:10.1007/s00209-005-0895-5
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/121922
dc.subjectMathematical Physics
dc.subjectDisordered Systems and Neural Networks
dc.subjectProbability
dc.subjectSpectral Theory
dc.subject47B80; 34B45; 05C80
dc.titleSpectral properties of the Laplacian on bond-percolation graphs
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