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Partial differential equations with random inputs have become popular modelsto characterize physical systems with uncertainty coming from, e.g., imprecisemeasurement and intrinsic randomness. In this paper, we perform asymptotic rareevent analysis for such elliptic PDEs with random inputs. In particular, weconsider the asymptotic regime that the noise level converges to zerosuggesting that the system uncertainty is low, but does exists. We developsharp approximations of the probability of a large class of rare events.

Moderate Deviation for Random Elliptic PDEs with Small Noise