Bootstrap Multiscale Analysis and Localization¶in Random Media

By F. Germinet, A. Klein. 2001

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Schrödinger operators with dynamically defined potentials (2014, background): “This connection was developed further in several papers; see, for example, [87, 112].”
On localization in the continuous Anderson-Bernoulli model in higher dimension (2005, background): “As pointed out by A. Klein to the authors, our Lemma 4.18 (initial step) and Proposition A does not provide the hypothesis for [ GK1 , Th. 5.2] or [K, Th. 5.7] to conclude the localization theorem and further arguments seem needed.”
Moment analysis for localization in random Schrödinger operators (2003, methodology): “The existing results on localization in the continuum of dimension larger than one have been based on the multiscale analysis, first obtained for discrete operators [30,25,29,69,74] and then extended to the continuum [50, 18,32].”
Localization (2019, unknown): “In some sense, the strongest version of MSA known to work with unbounded operators is the boot-strap MSA developed by Germinet and Klein in [GK01]; stronger versions have since appeared (see e.g. [BK05, GK12, DS20, RZ23]), but to our knowledge the arguments bridging from the very weak Green’s…”
Operator kernel estimates for functions of generalized Schrödinger operators (2002, background): “Operator kernels avoid many technical problems associated with integral kernels; they have proved very useful in the study of Anderson localization of random Schrödinger operators and classical wave operators [2, 7, 8, 9, 13, 14].”