Emergence of anomalous distributions in disordered systems

The present day non-gaussian distribution of mass density of the universe evolved from an initial gaussian distribution in the presence of nonlinear interactions. We discuss an analog in disordered condensed matter system where Increasing the disorder changes the distribution of conductances from a gaussian at weak disorder to a log-normal at strong disorder. The highly asymmetric "one-sided" log-normal distribution in the intermediate crossover regime can be understood as a simple hybrid of these two limiting distributions.