Conditional exponential directed last passage percolation under a one-point upper large deviation event

Under typical scaling, the last passage time field of the directed last passage percolation model with exponential site distributions converges to the KPZ fixed point.

In this paper, we consider an atypical scenario in which the last passage time to a specific site is unusually large, and we explore how the last passage time field changes under this one-point upper large deviation event.

We prove a conditional law of large numbers and compute the limiting fluctuations in certain regimes.

Our proofs rely on an analysis of explicit multi-point distributions.