Convergence of Half-Space Last Passage Percolation Away from the Boundary to the Directed Landscape

TL;DR

This paper proves that the half-space exponential last passage percolation model converges to the directed landscape away from the boundary, using coupling techniques and deviation estimates, extending the understanding of LPP models in half-spaces.

Contribution

It introduces a coupling approach between half-space and full-space LPP models and establishes convergence to the directed landscape away from the boundary.

Findings

Half-space LPP converges to the directed landscape away from the boundary.

Coupling method effectively relates half-space and full-space LPP models.

Moderate deviation estimates support the convergence proof.

Abstract

In this note, we prove convergence of the half-space exponential last passage percolation (LPP) model, away from the boundary, to the directed landscape. Our approach couples the half-space and full-space LPP models and constructs two barrier events based on the monotonicity of last passage paths. Combining this coupling with moderate deviation estimates for both models and the known convergence of full-space LPP to the directed landscape, we establish the desired convergence.