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Finite Time Corrections in KPZ Growth Models

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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.

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  1. Institute for Applied Mathematics, University of Bonn, Endenicher Allee 60, 53115, Bonn, Germany

    Patrik L. Ferrari & René Frings

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  1. Patrik L. Ferrari
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  2. René Frings
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Correspondence to Patrik L. Ferrari.

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Ferrari, P.L., Frings, R. Finite Time Corrections in KPZ Growth Models. J Stat Phys 144, 1123 (2011). https://doi.org/10.1007/s10955-011-0318-4

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  • DOI: https://doi.org/10.1007/s10955-011-0318-4

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