  In this paper, we use recent breakthroughs in the study of coupled
subwavelength resonator systems to reveal new insight into the mechanisms
responsible for the fundamental features of Anderson localization. The
occurrence strong localization in random media has proved difficult to
understand, particularly in physically derived multi-dimensional models and
systems with long-range interactions. We show here that the scattering of
time-harmonic waves by high-contrast resonators with randomly chosen material
parameters reproduces the characteristic features of Anderson localization. In
particular, we show that the hybridization of subwavelength resonant modes is
responsible for both the repulsion of energy levels as well as the widely
observed phase transition, at which point eigenmode symmetries swap and very
strong localization is possible. We derive results from first principles, using
asymptotic expansions in terms of the material contrast parameter and obtain a
characterization of the localized modes in terms of generalized capacitance
matrices. This model captures the long-range interactions of the
wave-scattering system and provides a concise framework to explain the exotic
phenomena that are observed.

Disordered Systems and Neural Networks;Analysis of PDEs;Optics