Random Words, Toeplitz Determinants and Integrable Systems. I
- Author(s): Its, Alexander R.;
- Tracy, Craig A.;
- Widom, Harold
- et al.
Published Web Locationhttps://arxiv.org/pdf/math/9909169.pdf
It is proved that the limiting distribution of the length of the longest weakly increasing subsequence in an inhomogeneous random word is related to the distribution function for the eigenvalues of a certain direct sum of Gaussian unitary ensembles subject to an overall constraint that the eigenvalues lie in a hyperplane.