UNIVERSALITY OF THE GEODESIC TREE IN LAST PASSAGE PERCOLATION

In this paper, we consider the geodesic tree in exponential last passage percolation. We show that for a large class of initial conditions around the origin, the line-to-point geodesic that terminates in a cylinder located around the point (N, N), and whose width and length are o(N-2/3) and o(N), respectively, agrees in the cylinder, with the stationary geodesic sharing the same end-point. In the case of the point-to-point model where the geodesic starts from the origin, we consider width delta N-2/3, length up to delta(3/2) N/(log(delta(-1)))(3), and provide lower and upper bounds for the probability that the geodesics agree in that cylinder.

Automated summary

This paper investigates the geodesic tree in exponential last passage percolation and demonstrates the probability of the overlap between geodesics and stationary geodesics within a cylinder under certain conditions.