  It has been shown by Pittel and Romik that the random surface associated with
a large rectangular Young tableau converges to a deterministic limit. We study
the fluctuations from this limit along the edges of the rectangle. We show that
in the corner, these fluctuations are gaussian wheras, away from the corner and
when the rectangle is a square, the fluctuations are given by the Tracy-Widom
distribution. Our method is based on a connection with the Jacobi ensemble.
