We consider the evolution of the probability distribution $\pp (\chi ,\chib,\t)$, associated with an inhomogeneous light scalar field $\chi$ in theRobertson-Walker Universe, where the inhomogeneities are produced by quantumfluctuations during an earlier inflationary epoch. For a specific choice ofscalar potential which occurs in models of so called late-time phasetransitions in which domain walls are produced, $\pp$ is shown to evolve from aGaussian to a non-Gaussian distribution. The structure of the latter justifiesthe recent use of 3-dimensional percolation theory to describe the initialdistribution of domain walls in these models.
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