Uniformity transition for ray intensities in random media. (15th March 2018) - Pradas, Marc; Pumir, Alain; Wilkinson, Michael
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 x k, representing successive focussing or de-focussing events. The number of ray trajectories reaching a given point is assumed to proliferate exponentially: 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 → ∞, and a phase where the S has large fluctuations, for which we provide a large deviation analysis.