In the directed landscape, shock structures of eternal solutions reconstruct the instability region of the KPZ fixed point, and all semi-infinite geodesic configurations from any space-time point fall into exactly twenty networks.
The KPZ equation and the directed landscape
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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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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.