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| HAL: hal-00551931, version 4 |
| arXiv: 1101.0900 |
| Detailed view |  Export this paper |
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| Available versions: | v1 (2011-01-05) | v2 (2011-05-24) | v3 (2011-06-08) | v4 (2012-01-22) |
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| Inverse tunneling estimates and applications to the study of spectral statistics of random operators on the real line |
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| Frédéric Klopp 1 |
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| (2011-01-05) |
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| We present a proof of Minami type estimates for one dimensional random Schrödinger operators valid at all energies in the localization regime provided a Wegner estimate is known to hold. The Minami type estimates are then applied to various models to obtain results on their spectral statistics. The heuristics underlying our proof of Minami type estimates is that close by eigenvalues of a one-dimensional Schrödinger operator correspond either to eigenfunctions that live far away from each other in space or they come from some tunneling phenomena. In the second case, one can undo the tunneling and thus construct quasi-modes that live far away from each other in space. |
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| 1: | Institut de Mathématiques de Jussieu (IMJ) |
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CNRS : UMR7586 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot |
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| Subject | : | Mathematics/Mathematical Physics Mathematics/Spectral Theory |
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| Random operators – Minami estimate – spectral statistics – tunneling effect |
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| hal-00551931, version 4 | |
| http://hal.archives-ouvertes.fr/hal-00551931 | |
| oai:hal.archives-ouvertes.fr:hal-00551931 | |
| From: Frédéric Klopp | |
| Submitted on: Saturday, 21 January 2012 13:53:22 | |
| Updated on: Sunday, 22 January 2012 17:57:33 | |
