The KPZ equation and the directed landscape

2023/01/02 by Wu, Xuan · 5 citations
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2301.00547

Abstract

This paper proves the convergence of the narrow wedge solutions of the KPZ equation to the Airy sheet and the directed landscape in the locally uniform topology. This is the first convergence result to the Airy sheet and the directed landscape established for a positive temperature model. We also give an independent proof for the convergence of the KPZ equation to the KPZ fixed point for general initial conditions in the locally uniform topology. Together with the directed landscape convergence, we show the joint convergence to the KPZ fixed point for multiple initial conditions.

Cited by

• van den Berg-Kesten--type correlation inequalities for disjoint polymers in the KPZ universality class
• Multipoint distributions of the KPZ fixed point with compactly supported initial conditions
• Limiting one-point fluctuations of the geodesic in the directed landscape near the endpoints when the geodesic length goes to infinity
• The discrete periodic Pitman transform: invariances, braid relations, and Burke properties
• Spatial decorrelation of KPZ from narrow wedge

Related

• Characterization of the directed landscape from the KPZ fixed point
• The heat and the landscape I
• Energy solutions of KPZ are unique
• Weak convergence of directed polymers to deterministic KPZ at high temperature
• Spatial decorrelation of KPZ from narrow wedge