Probability, Ergodic Theory, Mathematical Physics Seminar

Conditional limits of the KPZ fixed point with a large height at one location.

Ray Zhang, University of Kansas

Friday, March 17th, 2023
3:00 PM - 4:00 PM
Hylan 1106A

The Kardar-Parisi-Zhang (KPZ) fixed point is a universal space-time limit field of the models in the KPZ universality class. We consider the asymptomatic behavior of the KPZ fixed point when the height of one location becomes large. With the narrow-wedge (step) initial condition, we obtained a unified multipoint formula for the conditional field after a 1:2:3 dynamical scaling. In particular, there is a phase transition phenomenon for the conditional limit distribution near the given point. I will explain how the conditional field arises in the setting of the directed landscape, which is another central object in the KPZ universality. This is based on joint work with Zhipeng Liu, Ron Nissim and Yizao Wang.

Event contact: arjun dot krishnan at rochester dot edu