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The Airy line ensemble is a positive-integer indexed system of randomcontinuous curves whose finite dimensional distributions are given by themulti-line Airy process. It is a natural object in the KPZ universality class:for example, its highest curve, the Airy$_2$ process, describes after thesubtraction of a parabola the limiting law of the scaled energy of a geodesicrunning from the origin to a variable point on an anti-diagonal line in suchproblems as Poissonian last passage percolation. The ensemble of curvesresulting from the Airy line ensemble after the subtraction of the sameparabola enjoys a simple and explicit spatial Markov property, the BrownianGibbs property. In this paper, we employ the Brownian Gibbs property to make aclose comparison between the Airy line ensemble's curves after affine shift andBrownian bridge, proving the finiteness of a superpolynomially growing momentbound on Radon-Nikodym derivatives. We also determine the value of a naturalexponent describing in Brownian last passage percolation the decay inprobability for the existence of several near geodesics that are disjointexcept for their common endpoints, where the notion of `near' refers to a smalldeficit in scaled geodesic energy, with the parameter specifying this nearnesstending to zero. To prove both results, we introduce a technique that may beuseful elsewhere for finding upper bounds on probabilities of events concerningrandom systems of curves enjoying the Brownian Gibbs property. Several resultsin this article play a fundamental role in a further study of Brownian lastpassage percolation in three companion papers, [Ham17a,b,c], in which geodesiccoalescence and geodesic energy profiles are investigated in scaledcoordinates.

Brownian regularity for the Airy line ensemble, and multi-polymer watermelons in Brownian last passage percolation