  Observations of galaxy luminosity function at high redshifts typically focus
on fields of view of limited sizes preferentially containing bright sources.
These regions possibly are overdense and hence biased with respect to the
globally averaged regions. Using a semi-analytic model based on Choudhury &
Ferrara (2006) which is calibrated to match a wide range of observations, we
study the reionization and thermal history of the universe in overdense
regions. The main results of our calculation are: (i) Reionization and thermal
histories in the biased regions are markedly different from the average ones
because of enhanced number of sources and higher radiative feedback. (ii) The
galaxy luminosity function for biased regions is markedly different from those
corresponding to average ones. In particular, the effect of radiative feedback
arising from cosmic reionization is visible at much brighter luminosities.
(iii) Because of the enhanced radiative feedback within overdense locations,
the luminosity function in such regions is more sensitive to reionization
history than in average regions. The effect of feedback is visible for absolute
AB magnitude $M_{AB} \gtrsim -17$ at $z=8$, almost within the reach of present
day observations and surely to be probed by JWST. This could possibly serve as
an additional probe of radiative feedback and hence reionization at high
redshifts.
