This paper presents a new, short proof of the computation of the upper tail large deviation rate function for the Brownian directed percolation model. Through a distributional equivalence between the last passage time in this model and the largest eigenvalue in a random matrix drawn from the Gaussian Unitary Ensemble, this provides a new proof of a previously known result. The method leads to associated results for the stationary Brownian directed percolation model which have not been observed before.
"Upper tail large deviations in Brownian directed percolation." Electron. Commun. Probab. 24 1 - 10, 2019. https://doi.org/10.1214/19-ECP249