DENSITY AND VELOCITY CORRELATIONS OF PEAKS FROM RANDOM GAUSSIAN FLUCTUATIONS

We calculate the correlation function and pairwise velocities of densi ty peaks in a Gaussian random field and the resulting correlation func tion in redshift space. In order to take maximum advantage of existing symmetries, we use spherical harmonics and provide a systematic serie s expansion of the full peak-peak correlation function up to second or der. We evaluate second-order expansions primarily as a control on the accuracy of the linear terms. Our calculations provide a simple way t o implement more complicated biasing schemes as well. In linear order the underlying power spectrum is modified with a transfer function tha t contains quantities from the biasing constraint and yields an effect ive 'biasing factor'. This is more complicated than just a scale-indep endent constant, so that the power spectrum, the pairwise velocities o f peaks and the resulting power spectrum in redshift space are all con siderably different from those of random points. This affects determin ations of Omega(0).