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.
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.
|Full text:||(AM) Accepted Manuscript|
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|Full text:||(VoR) Version of Record|
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|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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