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We establish a one-to-one correspondence between virialized haloes and theirseeds, namely peaks with a given density contrast at appropriateGaussian-filtering radii, in the initial Gaussian random density field. Thisfixes a rigorous formalism for the analytic derivation of halo properties fromthe linear power spectrum of density perturbations in any hierarchicalcosmology. The typical spherically averaged density profile and mass functionof haloes so obtained match those found in numerical simulations.

Fixing a Rigorous Formalism for the Accurate Analytic Derivation of Halo Properties