CRITICAL LARGE DEVIATIONS FOR GAUSSIAN FIELDS IN THE PHASE-TRANSITION REGIME .1.

We investigate large deviations for the empirical distribution functional of a Gaussian random field on R(Zd), d greater than or equal to 3, in the phase transition regime. We first prove that the specific entropy governs an N-d volume order large deviation principle outside the Gibbsian class. Within the Gibbsian class we derive an N-d-2 capacity order large deviation principle with exact rate function, and we apply this result to the asymptotics of microcanonical ensembles. We also give a spins' profile description of the field and show that smooth profiles obey N-d-2 order large deviations, whereas discontinuous profiles obey N-d-1 surface order large deviations.