Abstract
The statistics of the average height fluctuation of the one-dimensional Kardar–Parisi–Zhang(KPZ)-type surface is investigated. Guided by the idea of local stationarity, we derivethe scaling form of the characteristic function in the early-time regime, with t time and N the system size, from the known characteristic function in the stationary state () of the single-step model derivable from a Bethe ansatz solution, and thereby find thescaling properties of the cumulants and the large deviation function in the early-timeregime. These results, combined with the scaling analysis of the KPZ equation, imply theexistence of the universal scaling functions for the cumulants and an universal largedeviation function. The analytic predictions are supported by the simulation results forthree different models in the KPZ class.
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