  A statistical theory of the coupling between a quantum emitter and
Anderson-localized cavity modes is presented based on a dyadic Green's function
formalism. The probability of achieving the strong light-matter coupling regime
is extracted for an experimentally realistic system composed of InAs quantum
dots embedded in a disordered photonic crystal waveguide. We demonstrate that
by engineering the relevant parameters that define the quality of light
confinement, i.e. the light localization length and the loss length, strong
coupling between a single quantum dot and an Anderson-localized cavity is
within experimental reach. As a consequence of disorder-induced light
confinement provides a novel platform for quantum electrodynamics experiments.
