Self-Averaged Scaling Limits for Random Parabolic Waves
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Self-Averaged Scaling Limits for Random Parabolic Waves

  • Author(s): Fannjiang, Albert C.
  • et al.

Published Web Location

https://arxiv.org/pdf/math-ph/0306001.pdf
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Abstract

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.

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