We study the luminosity function and the correlation function of about 1200 z \sim 4 Lyman break galaxies ( LBGs ) with i ^ { \prime } < 26 that are photometrically selected from deep BRi ^ { \prime } imaging data of a 618 arcmin ^ { 2 } area in the Subaru/XMM-Newton Deep Field taken with Subaru Prime Focus Camera .
The contamination and completeness of our LBG sample are evaluated , on the basis of the Hubble Deep Field-North ( HDF-N ) objects , to be 17 % and 45 % , respectively .
We derive the UV ( rest 1700Å ) luminosity functions ( LFs ) and find a large population of UV-luminous galaxies at z \sim 4 .
The LFs of the red and blue subsamples imply that the bright LBGs are redder in the UV continuum than the average color of the LBGs .
Then we calculate the correlation function over \theta = 2 ^ { \prime \prime } -1000 ^ { \prime \prime } and find that it is fitted fairly well by a power law , \omega ( \theta ) = A _ { \omega } \theta ^ { -0.8 } , with A _ { \omega } = 0.71 \pm 0.26 .
We estimate the correlation length r _ { 0 } ( in comoving units ) of the two-point spatial correlation function \xi ( r ) = ( r / r _ { 0 } ) ^ { -1.8 } to be r _ { 0 } = 2.7 ^ { +0.5 } _ { -0.6 } h ^ { -1 } Mpc ( \Omega _ { m } = 0.3 and \Omega _ { \Lambda } = 0.7 ) .
The correlation function shows an excess of \omega ( \theta ) on small scales ( \theta \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ < $% } } } 5 ^ { \prime \prime } ) , departing from the power-law fit at > 3 \sigma significance level .
Interpreting this as being due to galaxy mergers , we evaluate the fraction of galaxies undergoing mergers to be 3.0 \pm 0.9 \% , which is significantly smaller than those of galaxies at intermediate redshifts .