Journal of Statistical Physics, Vol. 99, Nos. 3/4, 2000. p. 769-781.
We analyze the asymptotic behavior of the rescaled solution to the linear Korteweg-de-Vries equation when the initial conditions are supposed to be random and weakly dependent. By means of the method of moments we prove
the Gaussianity of the limiting process and we present its correlation function. The same technique is applied to the analysis of another third-order heat-type equation.