Exact Scaling Functions for One-Dimensional Stationary KPZ Growth

2002/12/31 by Michael Praehofer, Michael Prähofer, Herbert Spohn · 26 citations
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1023/b:joss.0000019810.21828.fc

published as J. Stat. Phys. 115 (1-2), 255-279 (2004) · 24 pages, 6 figures, replaced with revised version

openalex publication_date 2004/03/17 · arxiv created 2004/04/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We determine the stationary two-point correlation function of the one-dimensional KPZ equation through the scaling limit of a solvable microscopic model, the polynuclear growth model. The equivalence to a directed polymer problem with specific boundary conditions allows one to express the corresponding scaling function in terms of the solution to a Riemann-Hilbert problem related to the Painleve II equation. We solve these equations numerically with very high precision and compare our, up to numerical rounding exact, result with the prediction of Colaiori and Moore [1] obtained from the mode coupling approximation.

Citations

• Riemann-Hilbert problems for last passage percolation
• Spin-spin correlation functions for the two-dimensional Ising model: Exact theory in the scaling region
• Large-distance and long-time properties of a randomly stirred fluid
• Limiting distributions for a polynuclear growth model with external sources

Cited by

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Related

• The Upper Critical Dimension of the KPZ Equation
• KPZ limit theorems
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