Anderson Localization for the hierarchical Anderson-Bernoulli model on $\mathbb{Z}^d$
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913050782597120 |
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| author | Liu, Shihe Shi, Yunfeng Zhang, Zhifei |
| author_facet | Liu, Shihe Shi, Yunfeng Zhang, Zhifei |
| contents | In this paper, we prove Anderson localization for a hierarchical Anderson-Bernoulli model on lattice with arbitrary dimension, where the potential is characterized by a geometric hierarchical structure combined with fluctuations induced by independent and identically distributed (i.i.d.) Bernoulli random variables. Our method is also applicable to proving a probabilistic unique continuation result on $\mathbb{Z}^d$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18989 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Anderson Localization for the hierarchical Anderson-Bernoulli model on $\mathbb{Z}^d$ Liu, Shihe Shi, Yunfeng Zhang, Zhifei Analysis of PDEs Mathematical Physics Probability In this paper, we prove Anderson localization for a hierarchical Anderson-Bernoulli model on lattice with arbitrary dimension, where the potential is characterized by a geometric hierarchical structure combined with fluctuations induced by independent and identically distributed (i.i.d.) Bernoulli random variables. Our method is also applicable to proving a probabilistic unique continuation result on $\mathbb{Z}^d$. |
| title | Anderson Localization for the hierarchical Anderson-Bernoulli model on $\mathbb{Z}^d$ |
| topic | Analysis of PDEs Mathematical Physics Probability |
| url | https://arxiv.org/abs/2604.18989 |