Busemann functions, geodesics, and the competition interface for directed last-passage percolation
Abstract
In this survey article we consider the directed last-passage percolation model on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside of the class of exactly solvable models. We show how stationary cocycles are constructed from queueing fixed points and how these cocycles characterize the limit shape, yield existence of Busemann functions in directions where the shape has some regularity, describe the direction of the competition interface, and answer questions on existence, uniqueness, and coalescence of directional semi-infinite geodesics, and on nonexistence of doubly infinite geodesics.
Cite
@article{arxiv.1804.05715,
title = {Busemann functions, geodesics, and the competition interface for directed last-passage percolation},
author = {Firas Rassoul-Agha},
journal= {arXiv preprint arXiv:1804.05715},
year = {2018}
}
Comments
This is a chapter in a forthcoming AMS Proceedings collection of expanded notes from the AMS Short Course "Random Growth Models," which took place in Atlanta, GA, at the AMS Joint Mathematics Meetings in January 2017. Editors: Michael Damron, Firas Rassoul-Agha, Timo Seppalainen