  We study theoretically and numerically a new kind of spatial correlation for
waves in disordered media. We define $C_{\Gamma}$ as the correlation function
of the fluorescent decay rate of an emitter at two different positions inside
the medium. We show that the amplitude and the width of $C_{\Gamma}$ provide
decoupled information on the structural correlation of the disordered medium
and on the local environment of the emitter. This result may stimulate the
emergence of new imaging and sensing modalities in complex media.
