Finite time corrections in KPZ growth models

TL;DR

This paper investigates the finite-time corrections in KPZ class models, identifying non-universal shifts and convergence rates, and analyzing the effects of asymmetry and discreteness on the models' fluctuations.

Contribution

It explicitly computes the first-order non-universal corrections and convergence rates for KPZ models, and examines the impact of asymmetry and discreteness on these corrections.

Findings

Finite-time corrections are a non-random shift of order t^{-1/3}.

After correction, convergence to the limit is of order t^{-2/3}.

The strength of asymmetry affects the presence of the shift.

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.