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In rough stochastic PDE theory of Hairer type, rough path lifts with respectto the space variable of two-parameter continuous Gaussian processes play amain role. A prominent example of such processes is the solution of thestochastic heat equation under the periodic condition. The main objective ofthis paper is to show that the law of the spatial lift of this processsatisfies a Schilder type large deviation principle on the continuous pathspace over a geometric rough path space.

Large deviation principle for certain spatially lifted Gaussian rough path