Zhipeng Liu: One-point distribution of the geodesic in directed last passage percolation
Time: Tue 2021-09-21 14.15
Location: Zoom, meeting ID: 698 3346 0369
Lecturer: Zhipeng Liu (University of Kansas)
In this talk, we will discuss the geodesic of the directed last passage percolation (DLPP) with iid exponential weights. We will show how to find the explicit one-point distribution and its limit in the KPZ scaling. This is the first formula of the one-point distribution of the point-to-point geodesics in the KPZ university class, and is believed to be universal for all the models in this class. Our method relies on a transition probability of the DLPP obtained by Johansson, some summation techniques developed by Baik and Liu, and a Cauchy-type summation identity found by Liu.