Hydrodynamics of the $t$-PNG model via a colored $t$-PNG model

Hindy Drillick; Yier Lin

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arXiv · 2204.11158

Hydrodynamics of the $t$-PNG model via a colored $t$-PNG model

Hindy Drillick·Yier Lin

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Abstract

The $t$-PNG model introduced in Aggarwal, Borodin, and Wheeler (2021) is a deformed version of the polynuclear growth (PNG) model. In this paper, we prove the hydrodynamic limit of the model using soft techniques. One key element of the proof is the construction of a colored version of the $t$-PNG model, which allows us to apply the superadditive ergodic theorem and obtain the hydrodynamic limit, albeit without identifying the limiting constant. We then find this constant by proving a law of large numbers for the $\alpha$-points, which generalizes Groeneboom (2001). Along the way, we construct the stationary $t$-PNG model and prove a version of Burke's theorem for it.

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BibTeX RIS

Hindy Drillick, Yier Lin. 2022-04-24. Hydrodynamics of the $t$-PNG model via a colored $t$-PNG model. https://arxiv.org/abs/2204.11158

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