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

Abstract

We consider the geodesic of the directed last passage percolation with iid exponential weights. We find the explicit one-point distribution of the geodesic location joint with the last passage times, and its limit as the parameters go to infinity under the KPZ scaling.

Corrected a sign typo in two equations (1.23) and (3.8). No other changes