SEMINAIRE MERCREDI 30 JUIN 2004
14 heures
Salle Séminaire 5
Centre de Physique Théorique
Marseille-Luminy

Peter MUELLER
Fakultaet und Institut fuer Mathematik
Ruhr-Universitaet Bochum

Titre: Spectral properties of Laplacians on bond-percolation graphs

Abstract: Bond-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.