Uniformity transition for ray intensities in random media

Pradas, Marc; Pumir, Alain and Wilkinson, Michael (2018). Uniformity transition for ray intensities in random media. Journal of Physics A: Mathematical and Theoretical, 51(15), article no. 155002.

DOI: https://doi.org/10.1088/1751-8121/aab161

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 N contributions from different trajectories, each of which is a product of N independent identically distributed random variables xk, representing successive focussing or de-focussing events. The number of ray trajectories reaching a given point is assumed to proliferate exponentially: N=ΛN, 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 → ∞, and a phase where the S has large fluctuations, for which we provide a large deviation analysis.

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