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In this paper, we study the effects of correlated random phases in theintensity of a superposition of $N$ wave-fields. Our results suggest thatregardless of whether the phase distribution is continuous or discrete if thephases are random correlated variables, we must observe a heavier taildistribution and the emergence of extreme events as the correlation betweenphases increases. We believe that such a simple method can be easily applied inother situations to show the existence of extreme statistical events in thecontext of nonlinear complex systems.

A simple study of the correlation effects in the superposition of waves of electric fields: the emergence of extreme events