The directed landscape seen from its trees
Probability
2025-08-05 v2 Mathematical Physics
math.MP
Abstract
A basic question about the directed landscape is how much of it can be reconstructed simply by knowing the shapes of its geodesics. We prove that the directed landscape can be reconstructed from the shapes of its semi-infinite geodesics. In order to show this result, we make use of the Busemann process of the directed landscape together with a novel ``coordinate system" and ``differential distance" to capture the behaviour of semi-infinite geodesics.
Cite
@article{arxiv.2410.19070,
title = {The directed landscape seen from its trees},
author = {Mustazee Rahman and Balint Virag},
journal= {arXiv preprint arXiv:2410.19070},
year = {2025}
}
Comments
final version