  The Peregrine soliton is often considered as a prototype of the rogue waves.
After recent advances in the semi-classical limit of the 1-D focusing Nonlinear
Schr\"odinger (NLS) equation this conjecture can be seen from another
perspective. In the present paper, connecting deterministic and statistical
approaches, we numerically demonstrate the effect of the universal local
appearance of Peregrine solitons on the evolution of statistical properties of
random waves. Evidences of this effect are found in recent experimental studies
in the contexts of fiber optics and hydrodynamics. The present approach can
serve as a powerful tool for the description of the transient dynamics of
random waves and provide new insights into the problem of the rogue waves
formation.
