Upper tail large deviations of the directed landscape
Abstract
Starting from one-point tail bounds, we establish an upper tail large deviation principle for the directed landscape at the metric level. Surprisingly, at this higher level, the theory suggested by Jensen and Varadhan is significantly simplified. Metrics of finite rate are in one-to-one correspondence with measures supported on a set of countably many paths, and the rate function is given by a certain Kruzhkov entropy of these measures. As an application of our main result, we prove a large deviation principle for the directed geodesic.
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Publication details
- Journal / source
- Duke Mathematical Journal
- Publisher
- Duke University Press
- Volume
- 175
- Issue
- 13
- Pages
- 2425–2493
- Publication date
- 15 September 2026
- Language
- EN