Fluctuations of a one-dimensional polynuclear growth model in a half space

Abstract

We consider the multi-point equal time height fluctuations of a one-dimensional polynuclear growth model in a half space. For special values of the nucleation rate at the origin, the multi-layer version of the model is reduced to a determinantal process, for which the asymptotics can be analyzed. In the scaling limit, the fluctuations near the origin are shown to be equivalent to those of the largest eigenvalue of the orthogonal/symplectic to unitary transition ensemble at soft edge in random matrix theory.

arXiv comment51 pages, 8 figures

References in corpus (19)

• Level-Spacing Distributions and the Airy Kernel
• Shape Fluctuations and Random Matrices
• On Orthogonal and Symplectic Matrix Ensembles
• Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices
• Discrete polynuclear growth and determinantal processes
• Level-Spacing Distributions and the Airy Kernel
• Exact scaling functions for one-dimensional stationary KPZ growth
• Correlation Functions, Cluster Functions and Spacing Distributions for Random Matrices
• Correlations for the orthogonal-unitary and symplectic-unitary transitions at the hard and soft edges
• Statistical Self-Similarity of One-Dimensional Growth Processes
• Differential Equations for Dyson Processes
• Scale Invariance of the PNG Droplet and the Airy Process
• Dynamical Correlations among Vicious Random Walkers
• Vicious Random Walkers and a Discretization of Gaussian Random Matrix Ensembles
• Limiting distributions for a polynuclear growth model with external sources
• Universal Parametric correlations at the soft edge of the spectrum of random matrix ensembles
• Limit Theorems for Height Fluctuations in a Class of Discrete Space and Time Growth Models
• Fluctuations in the composite regime of a disordered growth model
• A PDE for the joint distributions of the Airy Process

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