Year: 2026
Type: article
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.
Source: Duke Mathematical Journal
Authors: Sayan Das, Duncan Dauvergne, Bálint Virág
Institutions: University of Chicago, University of Toronto
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4399061651