Abstract
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.
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