 Press–Schechter formalism

The Press-Schechter formalism estimates dark matter halo abundance by comparing a smoothed linear density contrast with the linear spherical-collapse threshold. A Gaussian upper-tail probability supplies the collapsed fraction, with a factor of two in the original mass accounting. Differentiating that fraction by smoothing mass gives the Press-Schechter halo mass function. It connects initial fluctuations with object counts, while idealized spherical collapse and the treatment of nested regions limit its accuracy.^[ref]

The Press–Schechter formalism is a theoretical framework used in cosmology to describe the formation of structure in the universe, particularly the statistical properties of dark matter halos and galaxy formation. Developed by SLAC physicists William H. Press and Paul Schechter in 1974, this formalism provides a way to estimate the number density and mass distribution of bound systems, like galaxies and clusters of galaxies, from the primordial density fluctuations in the universe.