The directed landscape in half-space

TL;DR

This paper establishes that two models in the KPZ class converge to the same half-space directed landscape, characterizing its properties and stationary measures.

Contribution

It proves convergence of models to the half-space directed landscape and characterizes this limit via the half-space KPZ fixed point.

Findings

Models converge to the half-space directed landscape.

Characterization of the half-space directed landscape in terms of KPZ fixed point.

Explicit construction of stationary measures for various models.

Abstract

We prove that two half-space models in the KPZ universality class, exponential last-passage percolation and a family of Poisson-avoiding metrics generalizing colored TASEP, converge to a common scaling limit. This scaling limit is the directed landscape in half-space, a random directed metric in the half-plane indexed by a parameter which determines the strength of the boundary interaction. As part of our analysis, we characterize the half-space directed landscape in terms of the half-space KPZ fixed point, and prove convergence of geodesics. We also give an explicit construction of joint stationary measures (or horizons) in half-space for the log-gamma polymer, the KPZ equation, exponential and geometric last passage percolation, and the directed landscape itself.