Exponential Scaling Limit of the Single-Particle Anderson Model Via Adaptive Feedback Scaling

Abstract

We propose a twofold extension of the Germinet-Klein bootstrap multi-scale analysis (BMSA) for the Anderson models on graphs. First, we show, with the help of a single scaling algorithm, that power-law decay bounds at some initial scale imply an asymptotically exponential decay of eigenfunctions (EFs) and of EF correlators (EFCs), even on graphs (of polynomial growth) which do not fulfill the uniform scalability condition required for the existing BMSA techniques. We also show that the exponential scaling limit of the EFs and EFCs holds true for a class of marginal distributions of the random potential with regularity lower than Hölder continuity of any positive order.

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