Open Access
2022 When the geodesic becomes rigid in the directed landscape
Zhipeng Liu
Author Affiliations +
Electron. Commun. Probab. 27: 1-13 (2022). DOI: 10.1214/22-ECP484


When the value L of the directed landscape at a point (p;q) is sufficiently large, the geodesic from p to q is rigid and its location fluctuates of order L14 around its expectation. We further show that at a midpoint of the geodesic, the location of the geodesic and the value of the directed landscape after appropriate scaling converge to two independent Gaussians.

Funding Statement

The work was supported by the University of Kansas Start Up Grant, the University of Kansas New Faculty General Research Fund, Simons Collaboration Grant No. 637861, and NSF grant DMS-1953687.


We would like to thank Jinho Baik, Ivan Corwin, Duncan Dauvergne, and Bálint Virág for the comments and suggestions.


Download Citation

Zhipeng Liu. "When the geodesic becomes rigid in the directed landscape." Electron. Commun. Probab. 27 1 - 13, 2022.


Received: 13 June 2021; Accepted: 21 August 2022; Published: 2022
First available in Project Euclid: 29 August 2022

arXiv: 2106.06913
MathSciNet: MR4478126
zbMATH: 1505.60090
Digital Object Identifier: 10.1214/22-ECP484

Primary: 60K35

Keywords: directed landscape , Geodesic

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