Permutations Without Long Decreasing Subsequences and Random Matrices
نویسنده
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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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 14 شماره
صفحات -
تاریخ انتشار 2007