Thursdays at 2:30 PM either in 901 Van Vleck Hall or on Zoom
We usually end for questions at 3:20 PM.
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February 3, 2022, ZOOM: Zhipeng Liu (University of Kansas)
One-point distribution of the geodesic in directed last passage percolation
In the recent twenty years, there has been a huge development in understanding the universal law behind a family of 2d random growth models, the so-called Kardar-Parisi-Zhang (KPZ) universality class. Especially, limiting distributions of the height functions are identified for a number of models in this class. Different from the height functions, the geodesics of these models are much less understood. There were studies on the qualitative properties of the geodesics in the KPZ universality class very recently, but the precise limiting distributions of the geodesic locations remained unknown.
In this talk, we will discuss our recent results on the one-point distribution of the geodesic of a representative model in the KPZ universality class, the directed last passage percolation with iid exponential weights. We will give the explicit formula of the one-point distribution of the geodesic location joint with the last passage times, and its limit when the parameters go to infinity under the KPZ scaling. The limiting distribution is believed to be universal for all the models in the KPZ universality class. We will further give some applications of our formulas.
February 17, 2022, in person: Pax Kivimae (Northwestern University)
February 24, 2022, ZOOM: Lucas Benigni (University of Chicago)
March 3, 2022, in person: David Keating (UW-Madison)
March 10, 2022, format TBD: Qiang Wu (University of Illinois Urbana-Champaign)
March 24, 2022, in person: Sayan Das (Columbia University)
March 31, 2022, in person: Will Perkins (University of Illinois Chicago)
April 7, 2022, ZOOM: Eliza O'Reilly (Caltech)