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The statistics of the average height fluctuation of the one-dimensionalKardar-Parisi-Zhang(KPZ)-type surface is investigated. Guided by the idea oflocal stationarity, we derive the scaling form of the characteristic functionin the early-time regime, $t\ll N^{3/2}$ with $t$ time and $N$ the system size,from the known characteristic function in the stationary state ($t\gg N^{3/2}$)of the single-step model derivable from a Bethe Ansatz solution, and therebyfind the scaling properties of the cumulants and the large deviation functionin the early-time regime. These results, combined with the scaling analysis ofthe KPZ equation, imply the existence of the universal scaling functions forthe cumulants and an universal large deviation function. The analyticpredictions are supported by the simulation results for two different models.Comment: 3 figure

Universal fluctuation of the average height in the early-time regime of one-dimensional Kardar–Parisi–Zhang-type growth