  We compute correlation function of a superconducting order parameter in a
continuous model of a two-dimensional Josephson-junction array in the presence
of a weak Gaussian noise. When the Josephson coupling is large compared to the
charging energy the correlations in the Euclidian space decay exponentially at
low temperatures regardless of the strength of the noise. We interpret such a
state as a collective Cooper-pair insulator and argue that it resembles
properties of disordered superconducting films.

Superconductivity;Mesoscale and Nanoscale Physics