Context. Knowing the exact shape of the UV luminosity function of high-redshift galaxies is important in order to understand the star formation history of the early universe. However, the uncertainties, especially at the faint and bright ends of the LFs, are still significant. Aims. In this paper, we study the UV luminosity function of redshift z = 2.5 - 4.5 galaxies in 2.38 deg^2 of ALHAMBRA data with I <= 24. Thanks to the large area covered by ALHAMBRA, we particularly constrain the bright end of the luminosity function. We also calculate the cosmic variance and the corresponding bias values for our sample and derive their host dark matter halo masses. Methods. We use a novel methodology based on redshift and magnitude probability distribution functions (PDFs). This methodology robustly takes into account the uncertainties due to redshift and magnitude errors, shot noise and cosmic variance, and models the luminosity function in two dimensions (z; M_UV ). Results. We find an excess of bright ~ M*_UV galaxies as compared to the studies based on broad-band photometric data. However, our results agree well with the luminosity function of the magnitude-selected spectroscopic VVDS data. We measure high bias values, b ~ 8 - 10, that are compatible with the previous measurements considering the redshifts and magnitudes of our galaxies and further reinforce the real high-redshift nature of our bright galaxies. Conclusions. We call into question the shape of the luminosity function at its bright end; is it a double power-law as suggested by the recent broad-band photometric studies or rather a brighter Schechter function, as suggested by our multi-filter analysis and the spectroscopic VVDS data.
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