We present the large statistics of the galaxy effective radius R _ { e } in the rest-frame far-infrared ( FIR ) wavelength R _ { e ( FIR ) } obtained from 1627 Atacama Large Millimeter/submillimeter Array ( ALMA ) 1-mm band maps that become public by 2017 July .
Our ALMA sample consists of 1034 sources with the star-formation rate \sim 100 - 1000 M _ { \odot } { yr ^ { -1 } } and the stellar mass \sim 10 ^ { 10 } - 10 ^ { 11.5 } M _ { \odot } at z = 0 - 6 .
We homogeneously derive R _ { e ( FIR ) } and FIR luminosity L _ { FIR } of our ALMA sources via the uv -visibility method with the exponential disk model , carefully evaluating selection and measurement incompletenesses by realistic Monte-Carlo simulations .
We find that there is a positive correlation between R _ { e ( FIR ) } and L _ { FIR } at the > 99 \% significance level .
The best-fit power-law function , R _ { e ( FIR ) } \propto L _ { FIR } ^ { \alpha } , provides \alpha = 0.28 \pm 0.07 , and shows that R _ { e ( FIR ) } at a fixed L _ { FIR } decreases toward high redshifts .
The best-fit \alpha and the redshift evolution of R _ { e ( FIR ) } are similar to those of R _ { e } in the rest-frame UV ( optical ) wavelength R _ { e ( UV ) } ( R _ { e ( Opt . ) } ) revealed by Hubble Space Telescope ( HST ) studies .
We identify that our ALMA sources have significant trends of R _ { e ( FIR ) } \lesssim R _ { e ( UV ) } and R _ { e ( Opt . ) } , which suggests that the dusty starbursts take place in compact regions .
Moreover , R _ { e ( FIR ) } of our ALMA sources is comparable to R _ { e ( Opt . ) } of quiescent galaxies at z \sim 1 - 3 as a function of stellar mass , supporting the evolutionary connection between these two galaxy populations .
We also investigate rest-frame UV and optical morphologies of our ALMA sources with deep HST images , and find that \sim 30 - 40 % of our ALMA sources are classified as major mergers .
This indicates that dusty starbursts are triggered not only by the major mergers but also the other mechanism ( s ) .