THE 2-POINT CORRELATION-FUNCTION IN PANCAKE MODELS AND THE FAIR SAMPLE HYPOTHESIS

We analyze large two-dimensional slices generated by a pancake model for galaxy formation. We normalize these slices to a total box length of 1200 h-1 Mpc and extract point samples by a dynamical biasing method. These samples are considered to be statistically ''fair'' representatives of observed galaxy samples. As initial conditions we use power spectra with power n in the range -2 less-than-or-equal-to n less-than-or-equal-to +2 truncated at the high-frequency end, similar to HDM initial conditions. We analyze the dependence of the two-point correlation function on the biasing method used. Then, we compare the correlation function of the whole sample with that of the subsamples extracted from the whole at different scales. The luminous fraction of the overdensity in subsamples as well as the correlation function slope and amplitude reveal large sampling errors on typical scales of present all-sky surveys. We calculate the frequency distributions of the characteristics of the correlation function for each scale and spectral index and consider their rms and absolute deviations from the average values. We present a method to reject the ''fair sample hypothesis'' on the basis of these distributions. We also compare the results with standard intrinsic error estimates and find that the variations due to sample to sample fluctuations are substantially larger. Since the calculated deviations from the average are due to large-scale inhomogeneities, the results on sampling errors in truncated spectra also contribute to sampling errors in nontruncated power spectra.