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Finite time corrections in KPZ growth models

By Patrik L. Ferrari and René Frings

Abstract

We consider some models in the Kardar-Parisi-Zhang universality class, namely the polynuclear growth model and the totally/partially asymmetric simple exclusion process. For these models, in the limit of large time t, universality of fluctuations has been previously obtained. In this paper we consider the convergence to the limiting distributions and determine the (non-universal) first order corrections, which turn out to be a non-random shift of order t^{-1/3} (of order 1 in microscopic units). Subtracting this deterministic correction, the convergence is then of order t^{-2/3}. We also determine the strength of asymmetry in the exclusion process for which the shift is zero. Finally, we discuss to what extend the discreteness of the model has an effect on the fitting functions.Comment: 34 pages, 5 figures, LaTeX; Improved version including shift of PASEP height functio

Topics: Mathematical Physics, Condensed Matter - Statistical Mechanics, 82C22, 60K35, 15A52
Year: 2011
DOI identifier: 10.1007/s10955-011-0318-4
OAI identifier: oai:arXiv.org:1104.2129
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