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Bond-percolation graphs are random subgraphs of the d-dimensional

integer lattice generated by a standard Bernoulli bond-percolation

process. The

associated graph Laplacians, subject to Dirichlet or Neumann conditions at

cluster boundaries, represent bounded, self-adjoint, ergodic random

operators. They possess almost surely the

non-random spectrum [0,4d] and a self-averaging integrated density

of states. This integrated density of states is shown to exhibit Lifshits

tails at both spectral edges in the non-percolating phase. Depending

on the boundary condition and on the spectral edge, the Lifshits tail

discriminates between different cluster geometries (linear clusters

versus cube-like

clusters) which contribute the dominating eigenvalues. Lifshits tails

arising

from cube-like clusters continue to show up above the percolation

threshold.

In contrast, the other type of Lifshits tails cannot be observed in the

percolating

phase any more because they are hidden by van Hove singularities from the

percolating cluster.