Department of Mathematics
Self-Averaged Scaling Limits for Random Parabolic Waves
- Author(s): Fannjiang, Albert C.
- et al.
Published Web Locationhttps://arxiv.org/pdf/math-ph/0306001.pdf
We consider 6 types of scaling limits for the Wigner-Moyal equation of the parabolic waves in random media, the limiting cases of which include the radiative transfer limit, the diffusion limit and the white-noise limit. We show under fairly general assumptions on the random refractive index field that sufficient amount of medium diversity (thus excluding the white-noise limit) leads to statistical stability or self-averaging in the sense that the limiting law is deterministic and is governed by various transport equations depending on the specific scaling involved. We obtain 6 different radiative transfer equations as limits.