It has been shown by Pittel and Romik that the random surface associated with a large rectangular Youngtableau 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 whereas, away from the corner and when the rectangle isa square, the fluctuations are given by the Tracy-Widom distribution. Our method is based on a connection with theJacobi ensemble.
Discrete Mathematics & Theoretical Computer Science