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This is a Quantitative Study study.

October 19, 2025Open Access

Large Deviation Principle for Last Passage Percolation Models

Key Points

The study reveals a large deviation principle for last passage percolation models under the KPZ scaling.
Utilizing a framework from prior work, the authors establish metric-level large deviations in LPP models.
The findings allow for streamlined analysis of geodesic fluctuations in last passage percolation models.
This work expands understanding within the KPZ universality class, focusing on complex models without exact solvability.

Abstract

Study of the KPZ universality class has seen the emergence of universal objects over the past decade which arrive as the scaling limit of the member models. One such object is the directed landscape, and it is known that exactly solvable last passage percolation (LPP) models converge to the directed landscape under the KPZ scaling. Large deviations of the directed landscape on the metric level were recently studied in arXiv:2405.14924, which also provides a general framework for establishing such large deviation principle (LDP). The main goal of the article is to employ and tweak that framework to establish a LDP for LPP models at the metric level without assuming exact solvability. We then use the LDP on the metric level to establish a LDP for geodesics in these models, providing a streamlined way to study large transversal fluctuations of geodesics in these models.

Large Deviation Principle for Last Passage Percolation Models

Key Points

Abstract

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