2006/05/30 by Deok-Sun Lee, Deok‐Sun Lee, Doochul Kim · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Ansatz #Bethe ansatz #Complex Systems and Time Series Analysis #Cumulant #Function (biology) #Geometry #Large deviations theory #Mathematical physics #Mathematics #Physics #Rate function #Scaling #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Type (biology) #Zhàng #cond-mat.stat-mech
paper · pdf · doi:10.1088/1742-5468/2006/08/p08014
3 figures
arxiv created 2006/05/30 · openalex publication_date 2006/08/21 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 derive the 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 the scaling properties of the cumulants and the large deviation function in the early-time regime. These results, combined with the scaling analysis of the KPZ equation, imply the existence of the universal scaling functions for the cumulants and an universal large deviation function. The analytic predictions are supported by the simulation results for three different models in the KPZ class.