\(L^p\) norms and support of eigenfunctions on graphs. (English) Zbl 1442.82006
Summary: This article is concerned with properties of delocalization for eigenfunctions of Schrödinger operators on large finite graphs. More specifically, we show that the eigenfunctions have a large support and we assess their \(\ell^p\)-norms. Our estimates hold for any fixed, possibly irregular graph, in prescribed energy regions, and also for certain sequences of graphs such as \(N\)-lifts.
MSC:
| 82B44 | Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics |
| 82D30 | Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) |
| 47B80 | Random linear operators |
| 60H25 | Random operators and equations (aspects of stochastic analysis) |
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
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