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Summary form only given. Noise-sustained patterns have been recently predicted in several systems including a Kerr cavity and an optical parametric oscillator. In these systems a regime of convective instability can appear, in which a transverse pattern arises as a macroscopic manifestation of amplified and spatially structured quantum noise, with magnification factors of several order of magnitudes. We study quantum correlations in the convective regime of a degenerate type-I optical parametric oscillator (OPO) using a time dependent parametric approximation, in which the intracavity pump field is taken as a classical stochastic field.