We follow the evolution with sample thickness, of intensity statistics for localized light transmitted through layered media in a crossover from one to three dimensions occasioned by transverse disorder. The probability distribution of intensity changes from one dimensional to a mixture of a mesoscopic function of a single parameter, the statistical conductance, and a distribution of intensity for Gaussian waves. This suggests that the change to a universal statistics beyond 1D is associated with the topological change in the spatial field distribution.
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