%0 Journal Article %T Mass assembly in quiescent and star-forming galaxies since z=4 from UltraVISTA %A O. Ilbert %A H. J. McCracken %A O. Le Fevre %A P. Capak %A J. Dunlop %A A. Karim %A M. A. Renzini %A K. Caputi %A S. Boissier %A S. Arnouts %A H. Aussel %A J. Comparat %A Q. Guo %A P. Hudelot %A J. Kartaltepe %A J. P. Kneib %A J. K. Krogager %A E. Le Floc'h %A S. Lilly %A Y. Mellier %A B. Milvang-Jensen %A T. Moutard %A M. Onodera %A J. Richard %A M. Salvato %A D. B. Sanders %A N. Scoville %A J. Silverman %A Y. Taniguchi %A L. Tasca %A R. Thomas %A S. Toft %A L. Tresse %A D. Vergani %A M. Wolk %A A. Zirm %J Physics %D 2013 %I arXiv %R 10.1051/0004-6361/201321100 %X We estimate the galaxy stellar mass function and stellar mass density for star-forming and quiescent galaxies with 0.210^10.7Msun. For the mass function of the quiescent galaxies, we do not find any significant evolution of the high-mass end at z<1; however we observe a clear flattening of the faint-end slope. From z~3 to z~1, the density of quiescent galaxies increases over the entire mass range. Their comoving stellar mass density increases by 1.6 dex between z~3 and z~1 and by less than 0.2dex at z<1. We infer the star formation history from the mass density evolution and we find an excellent agreement with instantaneous star formation rate measurements at z<1.5, while we find differences of 0.2dex at z>1.5 consistent with the expected uncertainties. We also develop a new method to infer the specific star formation rate from the mass function of star-forming galaxies. We find that the specific star formation rate of 10^10Msun galaxies increases continuously in the redshift range 1