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.
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The Martin boundary coincides with the horofunction boundary in the directed landscape; it consists of eternal solutions with spatial growth rates, the minimal part is the Busemann functions, and every eternal solution is a max-plus convex combination of countably many Busemann functions.
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Shocks, instability, and the twenty networks of infinite geodesics in the Directed Landscape
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.
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The Martin boundary of the Directed Landscape
The Martin boundary coincides with the horofunction boundary in the directed landscape; it consists of eternal solutions with spatial growth rates, the minimal part is the Busemann functions, and every eternal solution is a max-plus convex combination of countably many Busemann functions.