Local convergence in $t$-PNG

Márton Balázs; Ruby Bestwick; Artem Borisov; Elnur Emrah; Jessica Jay

Paper

Local convergence in $t$-PNG

Abstract

We prove local convergence of the

-PNG model with zero boundary to the stationary

-PNG model, confirming a recent conjecture of Drillick and Lin (2024). The stationary

-PNG model is the one with both left and bottom boundaries of Poisson nucleations with rate parameters

and

, respectively, for some

. In the proof, we consider the trajectories of certain second class particles via a basic monotone coupling of three

-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).