  The rigorous analytical calculation of the diffusion coefficient is performed
for the chaotic motion of a particle in a set of longitudinal waves with random
phases and large amplitudes (~ A). A first step proves the existence of a
quasilinear diffusion on a time scale ~ A^{-2/3} \ln A. A second step uses this
property to extend the result to asymptotic times by introducing the
conditional probability distribution of position and velocity of an orbit at a
given time when they are known at a previous time.
