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

Chhita, Sunil; Ferrari, Patrik L.; Spohn, Herbert

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


Authors

Patrik L. Ferrari

Herbert Spohn



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.

Citation

Chhita, S., Ferrari, P. L., & Spohn, H. (2018). Limit distributions for KPZ growth models with spatially homogeneous random initial conditions. Annals of Applied Probability, 28(3), 1573-1603. https://doi.org/10.1214/17-aap1338

Journal Article Type Article
Acceptance Date Aug 10, 2017
Online Publication Date Jun 1, 2018
Publication Date Jun 1, 2018
Deposit Date Sep 21, 2017
Publicly Available Date Mar 29, 2024
Journal Annals of Applied Probability
Print ISSN 1050-5164
Publisher Institute of Mathematical Statistics
Peer Reviewed Peer Reviewed
Volume 28
Issue 3
Pages 1573-1603
DOI https://doi.org/10.1214/17-aap1338
Related Public URLs https://arxiv.org/abs/1611.06690

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