Local convergence in $t$-PNG
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917138621530112 |
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| author | Balázs, Márton Bestwick, Ruby Borisov, Artem Emrah, Elnur Jay, Jessica |
| author_facet | Balázs, Márton Bestwick, Ruby Borisov, Artem Emrah, Elnur Jay, Jessica |
| contents | 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 $\frac{1}{λ(1-t)}$ and $λ$, respectively, for some $λ>0$. 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10550 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local convergence in $t$-PNG Balázs, Márton Bestwick, Ruby Borisov, Artem Emrah, Elnur Jay, Jessica Probability Mathematical Physics 60K35, 60K37 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 $\frac{1}{λ(1-t)}$ and $λ$, respectively, for some $λ>0$. 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). |
| title | Local convergence in $t$-PNG |
| topic | Probability Mathematical Physics 60K35, 60K37 |
| url | https://arxiv.org/abs/2512.10550 |