One-point distribution of the geodesic in the directed last passage percolation

Abstract: 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 the models in this class. We will also discuss some applications of this formula, such as the rigidity of the geodesic when the limiting height function becomes extremely large.