14 citations · 44 across the 11 of their papers we have counts for
11 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…
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…
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…
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…
Optimal-order exit point bounds in exponential last-passage percolation via the coupling technique
Elnur Emrah, Christopher Janjigian, Timo Seppäläinen
We develop a new probabilistic method for deriving deviation estimates in directed planar polymer and percolation models. The key estimates are for exit points of geodesics as they…
Right-tail moderate deviations in the exponential last-passage percolation
Elnur Emrah, Chris Janjigian, Timo Seppäläinen
We study moderate deviations in the exponential corner growth model, both in the bulk setting and the increment-stationary setting. The main results are sharp right-tail bounds on…
Flats, spikes and crevices: the evolving shape of the inhomogeneous corner growth model
Elnur Emrah, Christopher Janjigian, Timo Seppäläinen
We study the macroscopic evolution of the growing cluster in the exactly solvable corner growth model with independent exponentially distributed waiting times. The rates of the exp…
Limit shape and fluctuations for exactly solvable inhomogeneous corner growth models
Elnur Emrah
We study a class of corner growth models in which the weights are either all exponentially or all geometrically distributed. The parameter of the distribution at site is $…
Large deviations for some corner growth models with inhomogeneity
Elnur Emrah, Chris Janjigian
We study an inhomogeneous generalization of the classical corner growth in which the weights are exponentially distributed with random parameters. Our main interest is in the quenc…
Limit shapes for inhomogeneous corner growth models with exponential and geometric weights
Elnur Emrah
We generalize the exactly solvable corner growth models by choosing the rate of the exponential distribution and the parameter of the geometric distribution at…