The relation between the galaxy stellar mass M_star and the dark matter halo mass M_h gives important information on the efficiency in forming stars and assembling stellar mass in galaxies. We present the stellar mass to halo mass ratio (SMHR) measur
ements at redshifts 2<z<5, obtained from the VIMOS Ultra Deep Survey. We use halo occupation distribution (HOD) modelling of clustering measurements on ~3000 galaxies with spectroscopic redshifts to derive the dark matter halo mass M_h, and SED fitting over a large set of multi-wavelength data to derive the stellar mass M_star and compute the SMHR=M_star/M_h. We find that the SMHR ranges from 1% to 2.5% for galaxies with M_star=1.3x10^9 M_sun to M_star=7.4x10^9 M_sun in DM halos with M_h=1.3x10^{11} M_sun} to M_h=3x10^{11} M_sun. We derive the integrated star formation efficiency (ISFE) of these galaxies and find that the star formation efficiency is a moderate 6-9% for lower mass galaxies while it is relatively high at 16% for galaxies with the median stellar mass of the sample ~7x10^9 M_sun. The lower ISFE at lower masses may indicate that some efficient means of suppressing star formation is at work (like SNe feedback), while the high ISFE for the average galaxy at z~3 is indicating that these galaxies are efficiently building-up their stellar mass at a key epoch in the mass assembly process. We further infer that the average mass galaxy at z~3 will start experiencing star formation quenching within a few hundred millions years.
We investigate the evolution of galaxy clustering for galaxies in the redshift range 2.0<$z$<5.0 using the VIMOS Ultra Deep Survey (VUDS). We present the projected (real-space) two-point correlation function $w_p(r_p)$ measured by using 3022 galaxies
with robust spectroscopic redshifts in two independent fields (COSMOS and VVDS-02h) covering in total 0.8 deg$^2$. We quantify how the scale dependent clustering amplitude $r_0$ changes with redshift making use of mock samples to evaluate and correct the survey selection function. Using a power-law model $xi(r) = (r/r_0)^{-gamma}$ we find that the correlation function for the general population is best fit by a model with a clustering length $r_0$=3.95$^{+0.48}_{-0.54}$ h$^{-1}$Mpc and slope $gamma$=1.8$^{+0.02}_{-0.06}$ at $z$~2.5, $r_0$=4.35$pm$0.60 h$^{-1}$Mpc and $gamma$=1.6$^{+0.12}_{-0.13}$ at $z$~3.5. We use these clustering parameters to derive the large-scale linear galaxy bias $b_L^{PL}$, between galaxies and dark matter. We find $b_L^{PL}$ = 2.68$pm$0.22 at redshift $z$~3 (assuming $sigma_8$ = 0.8), significantly higher than found at intermediate and low redshifts. We fit an HOD model to the data and we obtain that the average halo mass at redshift $z$~3 is $M_h$=10$^{11.75pm0.23}$ h$^{-1}$M$_{odot}$. From this fit we confirm that the large-scale linear galaxy bias is relatively high at $b_L^{HOD}$ = 2.82$pm$0.27. Comparing these measurements with similar measurements at lower redshifts we infer that the star-forming population of galaxies at $z$~3 should evolve into the massive and bright ($M_r$<-21.5) galaxy population which typically occupy haloes of mass $langle M_hrangle$ = 10$^{13.9}$ h$^{-1}$ $M_{odot}$ at redshift $z$=0.
