Ivan Veselic




Thursday, June 10, 2004 - 2:00pm


MSTB 254

We study the family of Hamiltonians which corresponds to the
adjacency operators on a percolation graph. We characterise the set of
energies which are almost surely eigenvalues with finitely supported
eigenfunctions. This set of energies is a dense subset of the algebraic
integers. The integrated density of states has discontinuities precisely
at this set of energies. We show that the convergence of the integrated
densities of states of finite box Hamiltonians to the one on the whole
space holds even at the points of discontinuity. For this we use an
equicontinuity-from-the-right argument. The same statements hold for the
restriction of the Hamiltonian to the infinite cluster. In this case we
prove that the integrated density of states can be constructed using local
data only. Finally we study some mixed Anderson-Quantum percolation models
and establish results in the spirit of Wegner, and Delyon and Souillard.