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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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.