Understanding how galaxy properties are linked to the dark matter halos they reside in, and how they co-evolve is a powerful tool to constrain the processes related to galaxy formation. The stellar-to-halo mass relation (SHMR) and its evolution over the history of the Universe provides insights on galaxy formation models and allows to assign galaxy masses to halos in N-body dark matter simulations. We use a statistical approach to link the observed galaxy stellar mass functions on the COSMOS field to dark matter halo mass functions from the DUSTGRAIN simulation and from a theoretical parametrization from z=0 to z=4. We also propose an empirical model to describe the evolution of the stellar-to-halo mass relation as a function of redshift. We calculate the star-formation efficiency (SFE) of galaxies and compare results with previous works and semi-analytical models.
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