When fast and slow interfaces grow together: connection to the half-space problem of the Kardar-Parisi-Zhang class

Abstract

We study height fluctuations of interfaces in the $(1+1)$-dimensional Kardar-Parisi-Zhang (KPZ) class, growing at different speeds in the left half and the right half of space. Carrying out simulations of the discrete polynuclear growth model with two different growth rates, combined with the standard setting for the droplet, flat, and stationary geometries, we find that the fluctuation properties at and near the boundary are described by the KPZ half-space problem developed in the theoretical literature. In particular, in the droplet case, the distribution at the boundary is given by the largest-eigenvalue distribution of random matrices in the Gaussian symplectic ensemble, often called the GSE Tracy-Widom distribution. We also characterize crossover from the full-space statistics to the half-space one, which arises when the difference between the two growth speeds is small.

7 pages, 7 figures

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Cited by in corpus (7)

• Half-space stationary Kardar-Parisi-Zhang equation
• Large fluctuations of a Kardar-Parisi-Zhang interface on a half-line
• Replica Bethe Ansatz solution to the Kardar-Parisi-Zhang equation on the half-line
• Delta-Bose gas on a half-line and the KPZ equation: boundary bound states and unbinding transitions
• Large fluctuations of a Kardar-Parisi-Zhang interface on a half-line: the height statistics at a shifted point
• Circular Kardar-Parisi-Zhang interfaces evolving out of the plane
• The KPZ equation in a half space with flat initial condition and the unbinding of a directed polymer from an attractive wall