IS THE UNIVERSE A FRACTAL - TESTS ON QUASAR SAMPLES

We have used several complete samples of quasars (450 objects in total) to gain information on the large-scale structure of the Universe at redshifts 0.4 < z < 2.2. We have evaluated the conditional density and the average density functions to establish that on scales larger than 12.5 h-1 Mpc the quasar distribution becomes homogeneous. The use of a more conventional and time-honoured technique such as the correlation function is therefore appropriate in the case of the present samples and equivalent to the conditional and average density functions. These latter functions allow us, however, to put slightly stronger constraints on the amplitude of clustering at large scales. Possible observational biases which could lead to incorrect conclusions on quasar clustering are discussed.