Fluctuation theory for radiative transfer in random media

We consider the effect of small scale random fluctuations of the constitutive coefficients on boundary measurements of solutions to radiative transfer equations. As the correlation length of the random oscillations tends to zero, the transport solution is well approximated by a deterministic, averaged, solution. In this paper, we analyze the random fluctuations to the averaged solution, which may be interpreted as a central limit correction to homogenization.With the inverse transport problem in mind, we characterize the random structure of the singular components of the transport measurement operator. In regimes of moderate scattering, such components provide stable reconstructions of the constitutive parameters in the transport equation. We show that the random fluctuations strongly depend on the decorrelation properties of the random medium.