The directed landscape

D Dauvergne, J Ortmann, B Virág - Acta Mathematica, 2022 - projecteuclid.org
The conjectured limit of last passage percolation is a scale-invariant, independent,
stationary increment process with respect to metric composition. We prove this for Brownian …

Infinite geodesics, competition interfaces and the second class particle in the scaling limit

M Rahman, B Virág - arXiv preprint arXiv:2112.06849, 2021 - arxiv.org
We establish fundamental properties of infinite geodesics and competition interfaces in the
directed landscape. We construct infinite geodesics in the directed landscape, establish their …

Thermodynamic limit for directed polymers and stationary solutions of the Burgers equation

Y Bakhtin, L Li - Communications on Pure and Applied …, 2019 - Wiley Online Library
The first goal of this paper is to prove multiple asymptotic results for a time‐discrete and
space‐continuous polymer model of a random walk in a random potential. These results …

Space-time stationary solutions for the Burgers equation

Y Bakhtin, E Cator, K Khanin - Journal of the American Mathematical …, 2014 - ams.org
We construct space-time stationary solutions of the $1 $ D Burgers equation with random
forcing in the absence of periodicity or any other compactness assumptions. More precisely …

Stationary cocycles and Busemann functions for the corner growth model

N Georgiou, F Rassoul-Agha… - Probability Theory and …, 2017 - Springer
We study the directed last-passage percolation model on the planar square lattice with
nearest-neighbor steps and general iid weights on the vertices, outside of the class of …

Geometry of geodesics through Busemann measures in directed last-passage percolation

C Janjigian, F Rassoul-Agha… - Journal of the European …, 2022 - ems.press
We consider planar directed last-passage percolation on the square lattice with general iid
weights and study the geometry of the full set of semi-infinite geodesics in a typical …

Geodesics and the competition interface for the corner growth model

N Georgiou, F Rassoul-Agha… - Probability Theory and …, 2017 - Springer
We study the directed last-passage percolation model on the planar integer lattice with
nearest-neighbor steps and general iid weights on the vertices, outside the class of exactly …

Ergodicity and synchronization of the Kardar-Parisi-Zhang equation

C Janjigian, F Rassoul-Agha, T Seppäläinen - arXiv preprint arXiv …, 2022 - arxiv.org
The Kardar-Parisi-Zhang (KPZ) equation on the real line is well-known to admit Brownian
motion with a linear drift as a stationary distribution (modulo additive constants). We show …

Scaling limit of multi-type invariant measures via the directed landscape

O Busani, T Seppäläinen… - International Mathematics …, 2024 - academic.oup.com
This paper studies the large scale limits of multi-type invariant distributions and Busemann
functions of planar stochastic growth models in the Kardar–Parisi–Zhang (KPZ) class. We …

BUSEMANN FUNCTIONS AND GIBBS MEASURES IN DIRECTED POLYMER MODELS ON ℤ²

C Janjigian, F Rassoul-Agha - The Annals of Probability, 2020 - JSTOR
We consider random walk in a space-time random potential, also known as directed random
polymer measures, on the planar square lattice with nearest-neighbor steps and general iid …