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The one-point distribution of the height for the continuumKardar-Parisi-Zhang (KPZ) equation is determined numerically using the mappingto the directed polymer in a random potential at high temperature. Using animportance sampling approach, the distribution is obtained over a large rangeof values, down to a probability density as small as $10^{-1000}$ in the tails.The short time behavior is investigated and compared with recent analyticalpredictions for the large-deviation forms of the probability of rarefluctuations, showing a spectacular agreement with the analytical expressions.The flat and stationary initial conditions are studied in the full space,together with the droplet initial condition in the half-space.

Probing the large deviations of the Kardar-Parisi-Zhang equation at short time with an importance sampling of directed polymers in random media