  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.
