Abstract:We prove local convergence of the $t$-PNG model with zero boundary to the stationary $t$-PNG model, confirming a recent conjecture of Drillick and Lin (2024). The stationary $t$-PNG model is the one with both left and bottom boundaries of Poisson nucleations with rate parameters $\frac{1}{\lambda(1-t)}$ and $\lambda$, respectively, for some $\lambda>0$. In the proof, we consider the trajectories of certain second class particles via a basic monotone coupling of three $t$-PNG processes, and adapt microscopic concavity ideas used in particle models (e.g., Balázs and Seppäläinen (2009)), as well as blocking measure bounds like in Ferrari, Kipnis and Saada (1991).
From: Marton Balazs [view email]
[v1]
Thu, 11 Dec 2025 11:30:53 UTC (73 KB)
[v2]
Wed, 2 Sep 2026 15:56:10 UTC (77 KB)
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