We provide a framework for proving convergence to the directed landscape, the central
object in the Kardar-Parisi-Zhang universality class. For last passage models, we show that …

We consider the colored asymmetric simple exclusion process (ASEP) and stochastic six
vertex (S6V) model with fully packed initial conditions; the states of these models can be …

The stationary horizon (SH) is a stochastic process of coupled Brownian motions indexed by
their real-valued drifts. It was first introduced by the first author as the diffusive scaling limit of …

The directed landscape is a random directed metric on the plane that arises as the scaling
limit of classical metric models in the KPZ universality class. Typical pairs of points in the …

The Directed Landscape, a random directed metric on the plane (where the first and the
second coordinates are termed spatial and temporal respectively), was constructed in the …

We establish fundamental properties of infinite geodesics and competition interfaces in the
directed landscape. We construct infinite geodesics in the directed landscape, establish their …

We show that geodesics in the directed landscape have 3/2-variation and that weight
functions along the geodesics have cubic variation. We show that the geodesic and its …

Let ht be the KPZ fixed point started from any initial condition that guarantees ht has a
maximum at every time t almost surely. For any fixed t, almost surely max⁡ ht is uniquely …

The parabolic Airy line ensemble AA is a central limit object in the KPZ (Kardar–Parisi–
Zhang) universality class and related areas. On any compact set K= 1,⋯, k× a, a+ t …

In 2002, Johansson conjectured that the maximum of the Airy 2 process minus the parabola
x 2 is almost surely achieved at a unique location [Joh03, Conjecture 1.5]. This result was …