  We establish a fundamental relationship between the averaged density of
states and the extinction mean free path of wave propagating in random media.
  From the principle of causality and the Kramers-Kronig relations, we show
that both quantities are connected by dispersion relations and are constrained
by a frequency sum rule. The results are valid under very general conditions
and should be helpful in the analysis of measurements of wave transport through
complex systems and in the design of randomly or periodically structured
materials with specific transport properties.
