Characterization of the directed landscape from the KPZ fixed point
Characterization of the directed landscape from the KPZ fixed point
We show that the directed landscape is the unique coupling of the KPZ fixed point from all initial conditions at all times satisfying three natural properties: independent increments, monotonicity, and shift commutativity. Equivalently, we show that the directed landscape is the unique directed metric on $\mathbb R^2$ with independent increments …