Galaxy formation history through hod model from euclid mock catalogs

Halo Occupation Distribution (HOD) is a model giving the average number of galaxies in a dark matter halo, function of its mass and other intrinsic properties, like distance from halo center, luminosity and redshift of its constituting galaxies. It is believed that these parameters could also be related to the galaxy history of formation. We want to investigate more this relation in order to test and better refine this model. To do that, we extract HOD indicators from EUCLID mock catalogs for different luminosity cuts and for redshifts ranges going from 0.1 < z < 3.0. We study and interpret the trends of indicators function of these variations and tried to retrace galaxy formation history following the idea that galaxy evolution is the combination rather than the conflict of the two main proposed ideas nowadays: the older hierarchical mass merger driven paradigm and the recent downsizing star formation driven approach.