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