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arXiv · 1711.02972

Uniformity Transition for Ray Intensities in Random Media

Marc Pradas·Alain Pumir·Michael Wilkinson
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Abstract

This paper analyses a model for the intensity of distribution for rays propagating without absorption in a random medium. The random medium is modelled as a dynamical map. After $N$ iterations, the intensity is modelled as a sum $S$ of ${\cal N}$ contributions from different trajectories, each of which is a product of $N$ independent identically distributed random variables $x_k$, representing successive focussing or de-focussing events. The number of ray trajectories reaching a given point is assumed to proliferate exponentially: ${\cal N}=Λ^N$, for some $Λ>1$. We investigate the probability distribution of $S$. We find a phase transition as parameters of the model are varied. There is a phase where the fluctuations of $S$ are suppressed as $N\to \infty$, and a phase where the $S$ has large fluctuations, for which we provide a large deviation analysis.

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Marc Pradas, Alain Pumir, Michael Wilkinson. 2017-11-08. Uniformity Transition for Ray Intensities in Random Media. https://doi.org/10.1088/1751-8121%2Faab161

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