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Multi-scale Analysis of Random Alloy Models with Summable Site Potentials of Infinite Range
Communications in Mathematical Physics ( IF 2.4 ) Pub Date : 2021-01-01 , DOI: 10.1007/s00220-020-03917-8
Victor Chulaevsky

We propose a reformulation of the probabilistic component of the Multi-Scale Analysis adapted to the alloy-type Anderson models with a non-negligible dependence at large distances due to an infinite range of the media-particle interaction. Despite a considerable wealth of results accumulated in the spectral theory of random operators with short-range potentials, much less is known about the alloy models with a slow (e.g., inverse polynomial) decay of interaction. Applied to the alloys with a power-law interaction, the new approach gives rise to stronger localization results than in prior works under an optimal assumption (summability) on the single-site potential.

中文翻译:

具有无限范围可累积位点电位的随机合金模型的多尺度分析

我们建议重新制定多尺度分析的概率分量,以适应​​合金型安德森模型,由于无限范围的介质 - 粒子相互作用,在远距离上具有不可忽略的依赖性。尽管在具有短程势的随机算子的谱理论中积累了相当丰富的结果,但对相互作用缓慢(例如,逆多项式)衰减的合金模型知之甚少。应用于具有幂律相互作用的合金,在单点电位的最佳假设(可和性)下,新方法产生比先前工作更强的定位结果。
更新日期:2021-01-01
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