Propagation of waves in a randomly inhomogeneous medium with strongly developed fluctuations. III. Arbitrary power-law noise correlation function

The investigation of the infrared behavior of the propagator of a light wave in a randomly inhomogeneous medium with massless Gaussian noise is continued. The infrared representation of the propagator proposed in [1] for correlation function $D_\varphi(k)\sim k^{-2}$ is generalized to the case of an arbitrary power-law noise correlation function and is rigorously established in the first two orders of the infrared asymptotic behavior by construction of a suitable $R$ operation. As a consequence, the results of [1] are generalized to the case of critical opalescence, when $D_\varphi(k)\sim k^{-2+\eta}$, where $\eta\approx0,03$ is the Fisher index.