Percolation Hamiltonians
arXiv:1002.5000
Abstract
There has been quite some activity and progress concerning spectral asymptotics of random operators that are defined on percolation subgraphs of different types of graphs. In this short survey we record some of these results and explain the necessary background coming from different areas in mathematics: graph theory, group theory, probability theory and random operators.
v3: final version, typos corrected; v2: references and some comments added; to appear in "Boundaries and spectra of random walks," proceedings of the Alp workshop Graz - St. Kathrein 2009, edited by D. Lenz, F. Sobieczky, W. Woess