Anderson-Bernoulli localization at large disorder on the 2D lattice. (English) Zbl 1494.82011
Summary: We consider the Anderson model at large disorder on \(\mathbb{Z}^2\) where the potential has a symmetric Bernoulli distribution. We prove that Anderson localization happens outside a small neighborhood of finitely many energies. These finitely many energies are Dirichlet eigenvalues of the minus Laplacian restricted on some finite subsets of \(\mathbb{Z}^2\).
MSC:
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
| 82B44 | Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics |
| 82B43 | Percolation |
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
| 60G60 | Random fields |
| 35P15 | Estimates of eigenvalues in context of PDEs |
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