Anderson Localization for the hierarchical Anderson-Bernoulli model on $\mathbb{Z}^d$

Fuente: arXiv
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Main Authors: Liu, Shihe, Shi, Yunfeng, Zhang, Zhifei
Format: Preprint
Published: 2026
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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