We present results of a survey for Ly \alpha emitters at z \approx 4.86 based on optical narrowband ( \lambda _ { c } = 7126 Å , \Delta \lambda = 73 Å ) and broadband ( B , V , r ^ { \prime } , i ^ { \prime } , and z ^ { \prime } ) observations of the Cosmic Evolution Survey ( COSMOS ) field using Suprime-Cam on the Subaru Telescope .
We find 79 LAE candidates at z \approx 4.86 over a contiguous survey area of 1.83 deg ^ { 2 } , down to the Ly \alpha line flux of 1.47 \times 10 ^ { -17 } { ergs s ^ { -1 } cm ^ { -2 } } .
We obtain the Ly \alpha luminosity function with a best-fit Schechter parameters of \log L ^ { * } = 42.9 ^ { +0.5 } _ { -0.3 } { ergs s ^ { -1 } } and \phi ^ { * } = 1.2 ^ { +8.0 } _ { -1.1 } \times 10 ^ { -4 } { Mpc ^ { -3 } } for \alpha = -1.5 ( fixed ) .
The two-point correlation function for our LAE sample is \xi ( r ) = ( r / 4.4 ^ { +5.7 } _ { -2.9 } { Mpc } ) ^ { -1.90 \pm 0.22 } .

In order to investigate the field-to-field variations of the properties of Ly \alpha emitters , we divide the survey area into nine tiles of 0.5 ^ { \circ } \times 0.5 ^ { \circ } each .
We find that the number density varies with a factor of \simeq 2 from field to field with high statistical significance .
However , we find no significant field-to-field variance when we divide the field into four tiles with 0.7 ^ { \circ } \times 0.7 ^ { \circ } each .
We conclude that at least 0.5 deg ^ { 2 } survey area is required to derive averaged properties of LAEs at z \sim 5 , and our survey field is wide enough to overcome the cosmic variance .