Below is the ascii version of the abstract for 05-176.
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Werner Kirsch, Peter Mueller
Spectral properties of the Laplacian 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.