Probability Seminar
Spring 2023
Thursdays at 2:30 PM either in 901 Van Vleck Hall or on Zoom
We usually end for questions at 3:20 PM.
ZOOM LINK. Valid only for online seminars.
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January 26, 2023, in person: Evan Sorensen (UW-Madison)
The stationary horizon as a universal object for KPZ models
The last 5-10 years has seen remarkable progress in constructing the central objects of the KPZ universality class, namely the KPZ fixed point and directed landscape. In this talk, I will discuss a third central object known as the stationary horizon (SH). The SH is a coupling of Brownian motions with drifts, indexed by the real line, and it describes the unique coupled invariant measures for the directed landscape. I will talk about how the SH appears as the scaling limit of several models, including Busemann processes in last-passage percolation and the TASEP speed process. I will also discuss how the SH helps to describe the collection of infinite geodesics in all directions for the directed landscape. Based on joint work with Timo Seppäläinen and Ofer Busani.