We consider the evolution of the probability distribution P(chi, chiBA
R, t), associated with an inhomogeneous light scalar field chi in the
Robertson-Walker Universe, where the inhomogeneities are produced by q
uantum fluctuations during an earlier inflationary epoch. For a specif
ic choice of scalar potential which occurs in models of so-called late
-time phase transitions in which domain walls are produced, P is shown
to evolve from a gaussian to a non-gaussian distribution. The structu
re of the latter justifies the recent use of three-dimensional percola
tion theory to describe the initial distribution of domain walls in th
ese models.