Quantum site percolation on amenable graphs

Abstract

We consider the quantum site percolation model on graphs with an amenable group action. It consists of a random family of Hamiltonians. Basic spectral properties of these operators are derived: non-randomness of the spectrum and its components, existence of an self-averaging integrated density of states and an associated trace-formula.

10 pages, LaTeX 2e, to appear in "Applied Mathematics and Scientific Computing", Brijuni, June 23-27, 2003. by Kluwer publishers

References in corpus (2)

• Spectral Analysis of Percolation Hamiltonians
• Integrated density of states for ergodic random Schrödinger operators on manifolds

Cited by in corpus (14)

• Spectral Analysis of Percolation Hamiltonians
• Spectral properties of the Laplacian on bond-percolation graphs
• Hamiltonians on discrete structures: Jumps of the integrated density of states and uniform convergence
• Lifshitz tails for spectra of Erdős--Rényi random graphs
• Sharpness of the phase transition and exponential decay of the subcritical cluster size for percolation on quasi-transitive graphs
• Uniform existence of the integrated density of states for models on $\ZZ^d$
• Integrated density of states and Wegner estimates for random Schrödinger Operators
• Uniform existence of the integrated density of states for random Schrödinger operators on metric graphs over ${\mathbb{Z}}^d$
• Continuity properties of the integrated density of states on manifolds
• Equality of Lifshitz and van Hove exponents on amenable Cayley graphs
• Spectral properties of Anderson-percolation Hamiltonians
• Uniform existence of the integrated density of states for combinatorial and metric graphs over Z^d
• Random Schrödinger Operators on discrete structures
• Groupoids, von Neumann Algebras and the Integrated Density of States