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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.

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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.

Item Type: Journal Item
Copyright Holders: 2018 IOP Publishing Ltd
ISSN: 1751-8121
Extra Information: 15 pp.
Keywords: random media; intensity fluctuations; phase transition; large deviations
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 54011
Depositing User: Marc Pradas
Date Deposited: 09 Apr 2018 10:02
Last Modified: 25 May 2019 23:22
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