Freak wave generation and decay is discussed in the context of the Hamiltonian description of ocean waves. In linear theory the probability distribution function (p.d.f.) of the surface elevation is given by the Normal distribution, while for finite amplitude waves there are, for extreme events, always deviations from the Normal, giving finite skewness and excess kurtosis. These deviations are caused by the presence of the bound waves and, in case of almost one-dimensional propagation, by non-resonant four-wave interactions.
Janssen, P. A. E. M. (2016). Hamiltonian description of ocean waves and freak waves. In Lecture Notes in Physics (Vol. 926, pp. 117–157). Springer Verlag. https://doi.org/10.1007/978-3-319-39214-1_5