author={Guillaume Bal and George C Papanicolaou and Leonid Ryzhik},
  journal={Stochastics and Dynamics},
We analyze the self-averaging properties of time-reversed solutions of the paraxial wave equation with random coefficients, which we take to be Markovian in the direction of propagation. This allows us to construct an approximate martingale for the phase space Wigner transform of two wave fields. Using a prioriL2-bounds available in the time-reversal setting, we prove that the Wigner transform in the high frequency limit converges in probability to its deterministic limit, which is the solution… 

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On the Self-Averaging of Wave Energy in Random Media

  • G. Bal
  • Mathematics
    Multiscale Model. Simul.
  • 2004
It is shown that wave energy is not stable, and instead scintillation is created by the wave dynamics, when the initial energy distribution is sufficiently singular.

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