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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4 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
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math.PR 4years
2026 4verdicts
UNVERDICTED 4representative citing papers
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.
Perturbed KPZ equation admits unique invariant measure absolutely continuous w.r.t. Brownian bridge with finite relative entropy and L^p Radon-Nikodym derivative for small perturbations.
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
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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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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 Gaussian structure of a perturbed KPZ
Perturbed KPZ equation admits unique invariant measure absolutely continuous w.r.t. Brownian bridge with finite relative entropy and L^p Radon-Nikodym derivative for small perturbations.
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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.