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Mathematics > Probability

arXiv:2204.11158 (math)
[Submitted on 24 Apr 2022 (v1), last revised 14 Dec 2022 (this version, v2)]

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

Authors: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.
Comments: 31 pages, 19 figures. Version to appear in AIHP
Subjects: Probability (math.PR); Mathematical Physics (math-ph)
MSC classes: 60F15 (Primary), 60J25 (Secondary)
Cite as: arXiv:2204.11158 [math.PR]
  (or arXiv:2204.11158v2 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.2204.11158

Submission history

From: Hindy Drillick [view email]
[v1] Sun, 24 Apr 2022 01:04:46 UTC (105 KB)
[v2] Wed, 14 Dec 2022 22:09:06 UTC (162 KB)
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