12/02/2025, 16:00 — 17:00 — Online
Lingfu Zhang, Caltech
From the KPZ Fixed Point to the Directed Landscape
Two core objects in the KPZ universality class are the KPZ fixed point (KPZFP) and the directed landscape (DL). They serve as the scaling limits of random growth processes and random planar geometry, respectively. Moreover, the KPZFP can be obtained as marginals of the DL. A central problem in this field is establishing convergence to both objects. This has been achieved for a few models with exactly solvable structures. Beyond exact solvability, only convergence to the KPZFP has been proven for general 1D exclusion processes. In this talk, I will discuss a recent work with Duncan Dauvergne that uncovers a new connection between these objects: the KPZFP uniquely characterizes the DL. Leveraging this fact, we establish convergence to the DL for a range of models, including some without exact solvability: general 1D exclusion processes, various couplings of ASEPs (e.g., the colored ASEP), the Brownian web and random walk web distances, and directed polymers.
Zoom link see here: https://spmes.impa.br
