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Limit distributions for KPZ growth models with spatially homogeneous random initial conditions.

Chhita, Sunil and Ferrari, Patrik L. and Spohn, Herbert (2018) 'Limit distributions for KPZ growth models with spatially homogeneous random initial conditions.', Annals of applied probability., 28 (3). pp. 1573-1603.

Abstract

For stationary KPZ growth in 1+1 dimensions, the height fluctuations are governed by the Baik–Rains distribution. Using the totally asymmetric single step growth model, alias TASEP, we investigate height fluctuations for a general class of spatially homogeneous random initial conditions. We prove that for TASEP there is a one-parameter family of limit distributions, labeled by the diffusion coefficient of the initial conditions. The distributions are defined through a variational formula. We use Monte Carlo simulations to obtain their numerical plots. Also discussed is the connection to the six-vertex model at its conical point.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1214/17-AAP1338
Date accepted:10 August 2017
Date deposited:25 September 2017
Date of first online publication:01 June 2018
Date first made open access:No date available

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