in Section \[sec:basic.notions\].

2.  In Section \[ssec:radial.descent\], we give a streamlined formulation of the main analytic tool of the MSA, allowing to establish exponential decay of eigenfunctions and Green functions in finite balls in absence of multiple “resonances”. A more traditional version of this technique, going back to [@FMSS85] and [@DK89], requires a number of additional, rather tedious (albeit elementary) geometrical arguments. (A reader familiar with [@DK89] may want to skip Section \[ssec:radial.descent\]). The two central notions of the new approach, allowing to simplify the MSA, are introduced in Section \[ssec:loc.tun\] (cf. Definitions \[def:loc\] and \[def:tun.IID\]).

3.  Section \[sec:SimpleScaleInd\] describes the simplified scale induction in a particular case of an IID random potential of large amplitude (“strong disorder”). Uniform bounds on eigenfunction correlators, obtained in the course of the scale induction, imply dynamical localization at any finite scale, with decay rate faster than polynomial, while a more traditional approach gives rise to a power-law decay.[^1]

4.  In Section \[sec:adapt.low.E\], we consider weakly disordered media where localization can be established only in a specific energy band (at “extreme energies”).

5.  In Section \[sec:adapt.mixing\], we adapt our method to lattice models with strongly mixing random potentials. Recall that the first results in 