Exponential scaling limit of the single-particle Anderson model via adaptive feedback scaling

Abstract: We propose a reformulation of the bootstrap version of the Multi-Scale Analysis (BMSA), developed by Germinet and Klein, to make explicit the fact that BMSA implies asymptotically exponential decay of eigenfunctions (EFs) and of EF correlators (EFCs), in the lattice Anderson models with diagonal disorder, viz. with an IID random potential. We also show that the exponential scaling limit of EFs and EFCs holds true for a class of marginal distributions of the random potential with regularity lower than H\"older continuity of any positive order.