3 papers
math.PR2025
Actions in the Airy line ensemble and convergence to the Airy sheet
Balint Virag, Xuan Wu
Actions in the Airy line ensemble represent distances from an infinitely far object. We characterize the Airy sheet by S(x,.)=T^x(.,1), where T^x is the unique action in the Airy l…
math.PR2025
Applications of optimal transport to Dyson Brownian Motions and beyond
Xuan Wu
We develop a new method based on Caffarelli's contraction theorem in optimal transport to obtain sharp and uniform modulus of continuity estimates for -Dyson Brownian motions w…
math.PR2025
The KPZ equation and the directed landscape
Xuan Wu
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…