Abstract

We investigate large deviations for the empirical distribution functional of a Gaussian random field on , in the phase transition regime. We first prove that the specific entropy governs an volume order large deviation principle outside the Gibbsian class. Within the Gibbsian class we derive an 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 order large deviations, whereas discontinuous profiles obey surface order large deviations.