Permutations Without Long Decreasing Subsequences and Random Matrices

نویسنده

  • Piotr Sniady
چکیده

ABSTRACT. We study the shape of the Young diagram λ associated via the Robinson–Schensted– Knuth algorithm to a random permutation in Sn such that the length of the longest decreasing subsequence is not bigger than a fixed number d; in other words we study the restriction of the Plancherel measure to Young diagrams with at most d rows. We prove that in the limit n → ∞ the rows of λ behave like the eigenvalues of a certain random matrix (traceless Gaussian Unitary Ensemble) with d rows and columns. In particular, the length of the longest increasing subsequence of such a random permutation behaves asymptotically like the largest eigenvalue of the corresponding random matrix.

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عنوان ژورنال:
  • Electr. J. Comb.

دوره 14  شماره 

صفحات  -

تاریخ انتشار 2007