  We study slowly moving solutions of the real Ginzburg-Landau equation on the
line, by a method due to J. Carr and R.L. Pego. These are functions taking
alternately positive or negative values on large intervals. A consequence of
our approach is that we can propose a rigorous derivation of a stochastic model
of coarsening by successive elimination of the smallest interval, which was
described in earlier work by A.J. Bray, B. Derrida and C. Godr\`eche.
