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3.4 Abundance of Dark Matter Halos 51 theory, it can be declared as a virialized object. Counting the number of such density peaks per unit volume is straightforward for a Gaussian probability distribution. To determine the abundance of halos at a redshift z, we use M , the density field smoothed on a mass scale M, as defined in section 3.1. Since M is distributed as a Gaussian variable with zero mean and standard deviation (M) [which depends only on the present linear power spectrum; see equation (3.7)], the probability that M is greater than some equals 1 2 d M exp - 2 M 2 (M) 2 (M) 1 = erfc . (3.16) 2 2 (M)