A limit distribution of the length of the longest ascent pair for a random permutation
نویسنده
چکیده
It is proved in [BOO], [J2] and [Ok1] that the joint distribution of suitably scaled rows of a partition with respect to the Plancherel measure of the symmetric group converges to the corresponding distribution of eigenvalues of a Hermitian matrix from the Gaussian Unitary Ensemble. We introduce a new measure on strict partitions, which is analogous to the Plancherel measure, and prove that the measure has a distribution similar to that of the Plancherel measure. In particular, we obtain that the limit distribution of the length of the longest ascent pair for a permutation is identical with the corresponding distribution of the length of the longest increasing subsequence.
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