We establish a fundamental relationship between the averaged local density of states and the extinction mean free path of waves 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 should be helpful in the analysis of wave transport through complex media and in the design of materials with specific transport properties.
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Carminati et al. (2009) studied this question.
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