Non-intersecting Brownian bridges and the Laguerre Orthogonal Ensemble

@article{Nguyen2015NonintersectingBB,
  title={Non-intersecting Brownian bridges and the Laguerre Orthogonal Ensemble},
  author={Gia Bao Nguyen and Daniel Remenik},
  journal={arXiv: Probability},
  year={2015}
}
We show that the squared maximal height of the top path among $N$ non-intersecting Brownian bridges starting and ending at the origin is distributed as the top eigenvalue of a random matrix drawn from the Laguerre Orthogonal Ensemble. This result can be thought of as a discrete version of K. Johansson's result that the supremum of the Airy$_2$ process minus a parabola has the Tracy-Widom GOE distribution, and as such it provides an explanation for how this distribution arises in models… 
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