Intensity distribution for waves in disordered media: Deviations from Rayleigh statistics

We study the intensity distribution function $P(I)$ for monochromatic waves propagating in a quasi-one-dimensional disordered medium, assuming that a point source and a point detector are embedded in the bulk of the medium. We find deviations from the Rayleigh statistics at moderately large I and a logarithmically normal asymptotic behavior of $P(I)$. When the radiation source and the detector are located close to the opposite edges of the sample (on a distance much less then the sample length), an intermediate regime with a stretched exponential behavior of $P(I)$ emerges.