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Pradas, Marc; Pumir, Alain and Wilkinson, Michael
(2018).
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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About
- Item ORO ID
- 54011
- Item Type
- Journal Item
- ISSN
- 1751-8121
- Extra Information
- 15 pp.
- Keywords
- random media; intensity fluctuations; phase transition; large deviations
- Academic Unit or School
-
Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM) - Copyright Holders
- © 2018 IOP Publishing Ltd
- Depositing User
- Marc Pradas