Fredholm Determinant Identity and the Convergence of Moments for Random Young Tableaux

@inproceedings{Baik2008FredholmDI,
  title={Fredholm Determinant Identity and the Convergence of Moments for Random Young Tableaux},
  author={Jinho Baik and Percy Deift and Eric M. Rains},
  year={2008}
}
We obtain an identity between Fredholm determinants of two kinds of operators, one acting on functions on the unit circle and the other acting on functions on a subset of the integers. This identity is a generalization of an identity between a Toeplitz determinant and a Fredholm determinant that has appeared in the random permutation context. Using this identity, we prove, in particular, convergence of moments for arbitrary rows of a random Young diagram under Plancherel measure.