Polynomial bound for the localization length of Lorentz mirror model on the 1D cylinder
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866910251022811136 |
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| author | Li, Linjun |
| author_facet | Li, Linjun |
| contents | We prove a polynomial upper bound for the localization length of the Lorentz mirror model and the Manhattan model on the even cylinder. The main input is a conditional cylinder-localization theorem in the winding regime: if short-direction crossings of $100n\times n$ rectangles have probability bounded below, then many closed trajectories wind around the cylinder. These winding trajectories are topological barriers and the localization follows from a two-switch surgery and double-counting argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_05900 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Polynomial bound for the localization length of Lorentz mirror model on the 1D cylinder Li, Linjun Probability Mathematical Physics We prove a polynomial upper bound for the localization length of the Lorentz mirror model and the Manhattan model on the even cylinder. The main input is a conditional cylinder-localization theorem in the winding regime: if short-direction crossings of $100n\times n$ rectangles have probability bounded below, then many closed trajectories wind around the cylinder. These winding trajectories are topological barriers and the localization follows from a two-switch surgery and double-counting argument. |
| title | Polynomial bound for the localization length of Lorentz mirror model on the 1D cylinder |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2010.05900 |