Localization for Random Schrödinger Operators Defined by Block Factors
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909575114915840 |
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| author | Damanik, David Gorodetski, Anton Kleptsyn, Victor |
| author_facet | Damanik, David Gorodetski, Anton Kleptsyn, Victor |
| contents | We consider discrete one-dimensional Schrödinger operators with random potentials obtained via a block code applied to an i.i.d. sequence of random variables. It is shown that, almost surely, these operators exhibit spectral and dynamical localization, the latter away from a finite set of exceptional energies. We make no assumptions beyond non-triviality, neither on the regularity of the underlying random variables, nor on the linearity, the monotonicity, or even the continuity of the block code. Central to our proof is a reduction to the non-stationary Anderson model via Fubini. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08153 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Localization for Random Schrödinger Operators Defined by Block Factors Damanik, David Gorodetski, Anton Kleptsyn, Victor Spectral Theory Mathematical Physics Dynamical Systems We consider discrete one-dimensional Schrödinger operators with random potentials obtained via a block code applied to an i.i.d. sequence of random variables. It is shown that, almost surely, these operators exhibit spectral and dynamical localization, the latter away from a finite set of exceptional energies. We make no assumptions beyond non-triviality, neither on the regularity of the underlying random variables, nor on the linearity, the monotonicity, or even the continuity of the block code. Central to our proof is a reduction to the non-stationary Anderson model via Fubini. |
| title | Localization for Random Schrödinger Operators Defined by Block Factors |
| topic | Spectral Theory Mathematical Physics Dynamical Systems |
| url | https://arxiv.org/abs/2504.08153 |