# Brownian Gibbs property for Airy line ensembles

@article{Corwin2011BrownianGP, title={Brownian Gibbs property for Airy line ensembles}, author={Ivan Corwin and Alan Hammond}, journal={Inventiones mathematicae}, year={2011}, volume={195}, pages={441-508} }

Consider a collection of N Brownian bridges $B_{i}:[-N,N] \to \mathbb{R} $, Bi(−N)=Bi(N)=0, 1≤i≤N, conditioned not to intersect. The edge-scaling limit of this system is obtained by taking a weak limit as N→∞ of the collection of curves scaled so that the point (0,21/2N) is fixed and space is squeezed, horizontally by a factor of N2/3 and vertically by N1/3. If a parabola is added to each of the curves of this scaling limit, an x-translation invariant process sometimes called the multi-line…

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