标题： 关于拟一维随机算符的安德森局域化 显示英文标题

标题： Anderson localisation for quasi-one-dimensional random operators

摘要： 1990年，Klein、Lacroix和Speis证明了宽度为$W \geqslant 1$的条状Anderson模型上的（光谱）Anderson局域化，允许势能分布具有奇异性。他们的证明除了采用多尺度分析外，还利用了随机矩阵乘积理论中的论证（正则分布情况已在Goldsheid和Lacroix的早期工作中通过其他方法处理）。我们给出了一个避免多尺度分析的证明，并将其扩展到一般的准一维模型，特别是允许随机跃迁。此外，我们证明了该模型的特征函数关联器的一个尖锐界，这表明了指数动力学局域化以及Fermi投影的指数衰减。我们的工作推广并补充了最近由Bucaj-Damanik-Fillman-Gerbuz-VandenBoom-Wang-Zhang、Jitomirskaya-Zhu、Gorodetski-Kleptsyn以及Rangamani在纯一维中发现的单尺度局域化证明（$W=1$）。 显示英文摘要

摘要： In 1990, Klein, Lacroix, and Speis proved (spectral) Anderson localisation for the Anderson model on the strip of width $W \geqslant 1$, allowing for singular distribution of the potential. Their proof employs multi-scale analysis, in addition to arguments from the theory of random matrix products (the case of regular distributions was handled earlier in the works of Goldsheid and Lacroix by other means). We give a proof of their result avoiding multi-scale analysis, and also extend it to the general quasi-one-dimensional model, allowing, in particular, random hopping. Furthermore, we prove a sharp bound on the eigenfunction correlator of the model, which implies exponential dynamical localisation and exponential decay of the Fermi projection. Our work generalises and complements the single-scale proofs of localisation in pure one dimension ($W=1$), recently found by Bucaj-Damanik-Fillman-Gerbuz-VandenBoom-Wang-Zhang, Jitomirskaya-Zhu, Gorodetski-Kleptsyn, and Rangamani.