We study the clustering properties of about 1200 z \sim 4 Lyman Break Galaxy ( LBG ) candidates with i ^ { \prime } < 26 which are selected by color 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 ( HDFN ) objects , to be 17 % and 45 % , respectively .
We derive the angular 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 then calculate the correlation length r _ { 0 } ( in comoving units ) of the two-point spatial correlation function \xi ( r ) = ( r / r _ { 0 } ) ^ { -1.8 } from A _ { \omega } using the redshift distribution of LBGs derived from the HDFN , and find r _ { 0 } = 2.7 ^ { +0.5 } _ { -0.6 } h ^ { -1 } Mpc in a \Lambda -dominated universe ( \Omega _ { m } = 0.3 and \Omega _ { \Lambda } = 0.7 ) .
This is twice larger than the correlation length of the dark matter at z \simeq 4 predicted from an analytic model by Peacock & Dodds but about twice smaller than that of bright galaxies predicted by a semi-analytic model of Baugh et al .
We find an excess of \omega ( \theta ) on small scales ( \theta \lesssim 5 ^ { \prime \prime } ) departing from the power law fit over 3 \sigma significance levels .
Interpreting this as due to galaxy mergers , we estimate the fraction of galaxies undergoing mergers in our LBG sample to be 3.0 \pm 0.9 \% , which is significantly smaller than those of galaxies at intermediate redshifts .