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Uniform Existence of the Integrated Density of States for Randomly Weighted Hamiltonians on Long-Range Percolation Graphs |
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| Authors: | Slim Ayadi Fabian Schwarzenberger Ivan Veselić |
| Affiliation: | 1. Departement of Mathematics, Faculté des Sciences de Tunis, University of Tunis El Manar, 2092, Tunis, Tunisia 2. Fakult?t für Mathematik, Technische Universit?t Chemnitz, 09107, Chemnitz, Germany |
| Abstract: | We consider random Hamiltonians defined on long-range percolation graphs over $mathbb {Z}^{d}$ . 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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