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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