Uniform existence of the integrated density of states for randomly weighted Hamiltonians on long-range percolation graphs
classification
🧮 math.SP
math-phmath.MP
keywords
densityexistencegraphshamiltoniansintegratedlong-rangepercolationrandom
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In this paper we consider random Hamiltonians defined on long-range percolation graphs over $\ZZ^d$. The Hamiltonian consists of a randomly weighted Laplacian plus a random potential. We prove uniform existence of the integrated density of states and express the IDS using a Pastur-Shubin trace formula.
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