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Atypically large fluctuations in macroscopic non-equilibrium systems continueto attract interest. Their probability can often be determined by the optimalfluctuation method (OFM). The OFM brings about a conditional variationalproblem, the solution of which describes the "optimal path" of the system whichdominates the contribution of different stochastic paths to the desiredstatistics. The OFM proved efficient in evaluating the probabilities of rareevents in a host of systems. However, theoretically predicted optimal pathswere observed in stochastic simulations only in diffusive lattice gases, wherethe predicted optimal density patterns are either stationary, or travel withconstant speed. Here we focus on the one-point height distribution of theparadigmatic Kardar-Parisi-Zhang interface. Here the optimal paths,corresponding to the distribution tails at short times, are intrinsicallynon-stationary and can be predicted analytically. Using the mapping to thedirected polymer in a random potential at high temperature, we obtain"snapshots" of the optimal paths in Monte-Carlo simulations which probe thetails with an importance sampling algorithm. For each tail we observe a verynarrow "tube" of height profiles around a single optimal path which agrees withthe analytical prediction. The agreement holds even at long times, supportingearlier assertions of the validity of the OFM in the tails well beyond theweak-noise limit.

Optimal paths of non-equilibrium stochastic fields: the Kardar-Parisi-Zhang interface as a test case