Polynuclear growth model, GOE${}^2$ and random matrix with deterministic source

Abstract

We present a random matrix interpretation of the distribution functions which have appeared in the study of the one-dimensional polynuclear growth (PNG) model with external sources. It is shown that the distribution, GOE${}^2$, which is defined as the square of the GOE Tracy-Widom distribution, can be obtained as the scaled largest eigenvalue distribution of a special case of a random matrix model with a deterministic source, which have been studied in a different context previously. Compared to the original interpretation of the GOE${}^2$ as ``the square of GOE'', ours has an advantage that it can also describe the transition from the GUE Tracy-Widom distribution to the GOE${}^2$. We further demonstrate that our random matrix interpretation can be obtained naturally by noting the similarity of the topology between a certain non-colliding Brownian motion model and the multi-layer PNG model with an external source. This provides us with a multi-matrix model interpretation of the multi-point height distributions of the PNG model with an external source.

27pages, 4 figures

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• On Time Correlations for KPZ Growth in One Dimension
• Non-Equilibrium Dynamics of Dyson's Model with an Infinite Number of Particles
• Infinite systems of non-colliding generalized meanders and Riemann-Liouville differintegrals
• Replica approach to the KPZ equation with half Brownian motion initial condition
• One-dimensional stochastic growth and Gaussian ensembles of random matrices
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• Nonstationary generalized TASEP in KPZ and jamming regimes
• Large deviations for the $q$-deformed polynuclear growth