Using the conditional luminosity function — the luminosity distribution of galaxies in a dark matter halo as a function of the halo mass — we present an empirical model to describe the redshift evolution of the rest B-band galaxy luminosity function ( LF ) .
The model is compared to various estimates of the LF , in rest UV- and B-bands , out to a redshift of 6 , including estimates of LFs of galaxy types separated to red and blue galaxies .
Using the observed LFs out to z \sim 5 , we present a general constraint on the redshift evolution of the central galaxy-halo mass relation .
The increase in the number density of luminous galaxies , at the bright-end of the LF , can be explained as due to a brightening of the luminosity of galaxies present in dark matter halo centers , relative to the luminosity of central galaxies in similar mass halos today .
The lack of strong evolution in the faint-end of the LF , however , argues against a model involving pure luminosity evolution at all halo mass scales .
The increase in luminosity at the bright-end compensates the rapid decline in the number density of massive halos as the redshift is increased .
The decline in group to cluster-mass dark matter halos out to a redshift of \sim 2 is not important as the central galaxy luminosity flattens at halo masses around 10 ^ { 13 } M _ { \hbox { $ \odot$ } } .
At redshifts \sim 2 to 3 , however , the density of bright galaxies begins to decrease due to the rapid decline in the number density of dark matter halos at mass scales around and below 10 ^ { 13 } M _ { \hbox { $ \odot$ } } .

Based on a comparison of our predictions to the measured UV LF of galaxies at redshifts \sim 3 , we estimate the probability distribution of halo masses to host Lyman break galaxies ( LBGs ) .
This probability for galaxies brighter than AB-absolute magnitudes of -21 , with a number density of \sim 5 \times 10 ^ { -3 } h ^ { 3 } Mpc ^ { -3 } , peaks at a halo mass of \sim 7 \times 10 ^ { 11 } h ^ { -1 } M _ { \hbox { $ \odot$ } } with a 68 % confidence level of ( 4 – 21 ) \times 10 ^ { 11 } h ^ { -1 } M _ { \hbox { $ \odot$ } } .
These estimates are consistent with the mass estimates for LBGs using two-point clustering statistics and recent estimates of halo masses based on spectroscopic observations .
For galaxies brighter than AB-absolute magnitudes of -21 at z \sim 6 , the halo mass scale is a factor of \sim 2 smaller ; the LF predictions at z \sim 6 are consistent with measured estimates in the literature .
Based on the models , we also predict the LF of galaxies at redshifts greater than 6 and also the bias factor of galaxies at redshifts greater than 3 ; these predictions will soon be tested with observational data .
In general , to explain high-redshift LFs , galaxies in dark matter halos around 10 ^ { 12 } M _ { \hbox { $ \odot$ } } must increase in luminosity by a factor of \sim 4 to 6 between today and redshift of 6 .