The work delivers the first full classification of extremal invariant measures for a half-space KPZ-class model and proves convergence to the Busemann process from arbitrary initial conditions with given slope.
The pinned half-space airy line ensemble
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Exponential last-passage percolation and Poisson-avoiding metrics converge to the directed landscape in half-space, characterized via the half-space KPZ fixed point with explicit stationary measures.
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Invariant measures for half-space geometric LPP: classification and the one force--one solution principle
The work delivers the first full classification of extremal invariant measures for a half-space KPZ-class model and proves convergence to the Busemann process from arbitrary initial conditions with given slope.
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The directed landscape in half-space
Exponential last-passage percolation and Poisson-avoiding metrics converge to the directed landscape in half-space, characterized via the half-space KPZ fixed point with explicit stationary measures.