2 papers
math.PR2026
Geodesic networks and the disjointness gap in the directed landscape
Duncan Dauvergne, Oliver Scott Pankratz
The directed landscape is a random directed metric on the plane that arises as the scaling limit of metric models in the KPZ universality class. For a pair of points p, q, the disj…
math.PR2025
Characterization of the directed landscape from the KPZ fixed point
Duncan Dauvergne, Lingfu Zhang
We show that the directed landscape is the unique coupling of the KPZ fixed point from all initial conditions satisfying three natural properties: independent increments, monotonic…