  We discuss the formation of large amplitude waves for sea states
characterized by JONSWAP spectra with random phases. In this context we discuss
experimental results performed in one of the largest wave tank facilities in
the world. We present experimental evidence that the tail of the cumulative
probability function of the wave heights for random waves strongly depends on
the ratio between the wave steepness and the spectral bandwidth. When this
ratio, called the Benjamin-Feir Index, is large the Rayleigh distribution
clearly underestimates the occurrence of large amplitude waves. Our
experimental results are also successfully compared with previously performed
numerical simulations of the Dysthe equation.
