## Science T1: Luminosity and mass functions

The luminosity and mass functions (LF/MF) are basic distributions and have been profusely studied by many extragalactic survey in the literature (see Johnston11 review). They provide the density number of galaxies of a given luminosity/mass at a given redshift, and permits to track the luminosity and mass evolution of the general red and blue populations. Because of their importance, the LF/MF are the starting point of any PROFUSE topic and an unbiased LF/MF estimator based on PDF techniques is mandatory.

In the next we describe the PROFUSE efforts to define the PDF-based estimator of the luminosity function and the stellar mass function, as well as the best observational approach to take advantage of the cosmic variance.

Using ALHAMBRA data, we are developing the posterior LF estimator based on PDFs. This estimator has important advantages with respect to previous ones, and will be applied to the J-PAS data in the future.

One fundamental uncertainty in any observational measurement derived from galaxy surveys is the relative cosmic variance (σ_{v}, also called sample variance), arising from the underlying large-scale density fluctuations and leading to variances larger than those expected from simple Poisson statistics. The most efficient way to tackle the cosmic variance is to split the survey into several independent areas on the sky.