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.
Exceptional force, uncountably many solutions in the KPZ fixed point.Preprint:arXiv:2505.09604, 2025
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
fields
math.PR 3years
2026 3verdicts
UNVERDICTED 3representative citing papers
Eternal solutions of the KPZ fixed point are completely classified as patchings of Busemann functions, with shocks at patch boundaries that coalesce forward in time and can form backward.
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.
citing papers explorer
-
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.
-
Classification of the eternal solutions and multiple coalescing shocks in the KPZ fixed point
Eternal solutions of the KPZ fixed point are completely classified as patchings of Busemann functions, with shocks at patch boundaries that coalesce forward in time and can form backward.
-
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.