Limiting distributions for a polynuclear growth model with external sources

Abstract

The purpose of this paper is to investigate the limiting distribution functions for a polynuclear growth model with two external sources, which was considered by Prähofer and Spohn. Depending on the strength of the sources, the limiting distribution functions are either the Tracy-Widom functions of random matrix theory, or a new explicit function which has the special property that its mean is zero. Moreover, we obtain transition functions between pairs of the above distribution functions in suitably scaled limits. There are also similar results for a discrete totally asymmetric exclusion process.

15 pages, 1 figure, LaTex

Cited by in corpus (23)

• Exact scaling functions for one-dimensional stationary KPZ growth
• A KPZ Cocktail- Shaken, not stirred: Toasting 30 years of kinetically roughened surfaces
• Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process
• Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals
• Stationary correlations for the 1D KPZ equation
• Fluctuations of a one-dimensional polynuclear growth model in a half space
• Renormalization fixed point of the KPZ universality class
• A stochastic Burgers equation from a class of microscopic interactions
• The 1+1-dimensional Kardar-Parisi-Zhang equation and its universality class
• Airy processes and variational problems
• Current fluctuations for anharmonic chains in thermal equilibrium
• From interacting particle systems to random matrices
• Finite-time fluctuations for the totally asymmetric exclusion process
• Nonintersecting random walks in the neighborhood of a symmetric tacnode
• Convergence of the two-point function of the stationary TASEP
• Reflected Brownian motions in the KPZ universality class
• Joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles
• Anomalous 1D fluctuations of a simple 2D random walk in a large deviation regime
• Painlevé Functions in Statistical Physics
• Stationary half-space last passage percolation
• Growth models, random matrices and Painleve transcendents
• Initial perturbation matters: implications of geometry-dependent universal Kardar-Parisi-Zhang statistics for spatiotemporal chaos
• Shock fluctuations for the Hammersley process