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
The directed landscape seen from its trees
Mustazee Rahman, Balint Virag
A basic question about the directed landscape is how much of it can be reconstructed simply by knowing the shapes of its geodesics. We prove that the directed landscape can be reco…
math.PR2024
KPZ fluctuations in the planar stochastic heat equation
Jeremy Quastel, Alejandro Ramirez, Balint Virag
We use a version of the Skorokhod integral to give a simple and rigorous formulation of the Wick-ordered (stochastic) heat equation with planar white noise, representing the free e…