  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 a previously known result. The
method leads to associated results for the stationary Brownian directed
percolation model which have not been observed before.
