a)–b) Histograms vs. the PDFs g(z_max) of the largest peak value from 5000 Gaussian random fields obtained by filtering a 256 × 256 discrete white noise map by means of a Gaussian filter with dispersion of 3.7 and 2.7 pixels in such a way as to reproduce approximately the noise in M1 and M2, respectively. Since each simulated map is characterized by a different number of peaks, the corresponding PDFs are slightly different from one another. For this reason, the displayed g(z_max) plotted in green corresponds to the mean number of peaks which are 384 and 960, respectively. In panel b the resulting PDF is in reasonably good agreement with the corresponding histogram, but a better result is obtainable if an effective number is used. To stress the fact that, although is about 17% smaller than N_p, the resulting PDF is only slightly different. All this is in accordance with the arguments in Sect. 3.