  We study the properties of Lyman-alpha emitters (LAEs) and Lyman-break
galaxies (LBGs) at z=3-6 using cosmological SPH simulations. We investigate two
simple scenarios for explaining the observed Ly-a and rest-frame UV luminosity
functions (LFs) of LAEs: (i) the "escape fraction" scenario, in which the
"effective" escape fraction (including the IGM attenuation) of Ly-a photons is
f_Lya ~0.1 (0.15) at z=3 (6), and (ii) the "stochastic" scenario, in which the
fraction of LAEs that are turned on at z=3 (6) is \Cstoc ~0.07 (0.2) after
correcting for the IGM attenuation. Our comparisons with a number of different
observations suggest that the stochastic scenario is preferred over the escape
fraction scenario. We find that the mean values of stellar mass, metallicity
and black hole mass hosted by LAEs are all smaller in the stochastic scenario
than in the escape fraction scenario. In our simulations, the galaxy stellar
mass function evolves rapidly, as expected in hierarchical structure formation.
However, its evolution is largely compensated by a beginning decline in the
specific star formation rate, resulting in little evolution of the rest-frame
UV LF from z=6 to 3. The rest-frame UV LF of both LAEs and LBGs at z=3 & 6 can
be described well by the stochastic scenario provided the extinction is
moderate, E(B-V) ~0.15, for both populations, although our simulation might be
overpredicting the number of bright LBGs at z=6. We also discuss the
correlation function and bias of LAEs. The Ly-a LFs at z=6 in a field-of-view
of 0.2 deg^2 show a significantly larger scatter owing to cosmic variance
relative to that in a 1 deg^2 field, and the scatter seen in the current
observational estimates of the Ly-a LF can be accounted for by cosmic variance.
