Duke Mathematical Journal· 2026Q1
Upper tail large deviations of the directed landscape
- 1citations
- Q1SCImago
- 2026year
Short summary
A new theory simplifies the understanding of the directed landscape's upper tail large deviations at the metric level, establishing a one-to-one correspondence between finite-rate metrics and measures on countably many paths.
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Key points
- Establishes an upper tail large deviation principle for the directed landscape at the metric level.
- Demonstrates a simplified theory compared to previous models (Jensen and Varadhan).
- Identifies a one-to-one correspondence between finite-rate metrics and measures on countably many paths.
- Defines the rate function via Kruzhkov entropy of these measures.
- Applies the main result to prove a large deviation principle for the directed geodesic.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Duke Mathematical Journal, 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics