5 papers
Local convergence in -PNG
Márton Balázs, Ruby Bestwick, Artem Borisov +2
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 -PN…
Critical fluctuations of last passage percolation with thick boundaries
Elnur Emrah, Patrik L. Ferrari, Min Liu
We consider the exponential last passage percolation (LPP) with thick two-sided boundary that consists of a few inhomogeneous columns and rows. Ben Arous and Corwin previously stud…
Anomalous geodesics in the inhomogeneous corner growth model
Elnur Emrah, Christopher Janjigian, Timo Seppäläinen
We study Busemann functions, semi-infinite geodesics, and competition interfaces in the exactly solvable last-passage percolation with inhomogeneous exponential weights. New phenom…
Permutation invariance in last-passage percolation and the distribution of the Busemann process
Erik Bates, Elnur Emrah, James Martin +2
In i.i.d. exponential last-passage percolation, we describe the joint distribution of Busemann functions, over all edges and over all directions, in terms of a joint last-passage p…
Coupling derivation of optimal-order central moment bounds in exponential last-passage percolation
Elnur Emrah, Nicos Georgiou, Janosch Ortmann
We introduce new probabilistic arguments to derive optimal-order central moment bounds in planar directed last-passage percolation. Our technique is based on couplings with the inc…