  We present a collective coordinate approach to study the collective behaviour
of a finite ensemble of $N$ stochastic Kuramoto oscillators using two degrees
of freedom; one describing the shape dynamics of the oscillators and one
describing their mean phase. Contrary to the thermodynamic limit $N\to\infty$
in which the mean phase of the cluster of globally synchronized oscillators is
constant in time, the mean phase of a finite-size cluster experiences Brownian
diffusion with a variance proportional to $1/N$. This finite-size effect is
quantitatively well captured by our collective coordinate approach.
