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

We analyze large two-dimensional slices generated by a pancake model f or galaxy formation. We normalize these slices to a total box length o f 1200 h-1 Mpc and extract point samples by a dynamical biasing method . These samples are considered to be statistically ''fair'' representa tives of observed galaxy samples. As initial conditions we use power s pectra 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 ini tial conditions. We analyze the dependence of the two-point correlatio n function on the biasing method used. Then, we compare the correlatio n function of the whole sample with that of the subsamples extracted f rom the whole at different scales. The luminous fraction of the overde nsity in subsamples as well as the correlation function slope and ampl itude reveal large sampling errors on typical scales of present all-sk y surveys. We calculate the frequency distributions of the characteris tics of the correlation function for each scale and spectral index and consider their rms and absolute deviations from the average values. W e present a method to reject the ''fair sample hypothesis'' on the bas is of these distributions. We also compare the results with standard i ntrinsic error estimates and find that the variations due to sample to sample fluctuations are substantially larger. Since the calculated de viations from the average are due to large-scale inhomogeneities, the results on sampling errors in truncated spectra also contribute to sam pling errors in nontruncated power spectra.