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$\begin{figure} \par\includegraphics[width=8.4cm,clip]{0278fig1.eps}\end{figure}$ Figure 1: Convergence of the mean energy of the ensemble averaged fields. The mean energy converges to the mean energy of the coherent field in the correlated case (dashed line). For the uncorrelated case, the mean energy converges to zero because the coherent field is zero in this case (full line). The mean energy is proportional to 1/N in the uncorrelated case, and results in a slope of -1 in the given log-log plot (thick line).
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0278fig2.eps}\vspace*{2mm} \includegraphics[width=8.8cm,clip]{0278fig3.eps}\end{figure}$ Figure 2: Ensemble averaged power spectra for the correlated case as function of frequency $\omega$ for different wavenumbers. The power maxima in the frequency spectra are close to the frequencies dictated by the unperturbed dispersion relation $\omega _0 = c_0 k$ . The bottom right panel shows the power spectrum of the ensemble averaged field (sampled at a specific time), showing a smooth distribution of energy over wavenumber.
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In the text

$\begin{figure} \par\includegraphics[width=6.9cm,clip]{0278fig4.eps}\end{figure}$ Figure 3: Relative frequency shifts for the correlated case (crosses) and for the uncorrelated case (squares). The frequency shifts are mostly positive in the uncorrelated case. In the correlated case, the shifts are much smaller and mostly negative.
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In the text

$\begin{figure} \par\includegraphics[width=6.9cm,clip]{0278fig4.eps}\end{figure}$	Figure 3: Relative frequency shifts for the correlated case (crosses) and for the uncorrelated case (squares). The frequency shifts are mostly positive in the uncorrelated case. In the correlated case, the shifts are much smaller and mostly negative.
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