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COMBINATORICS
2007

Permutations Without Long Decreasing Subsequences and Random Matrices

10 years 4 months ago
Permutations Without Long Decreasing Subsequences and Random Matrices
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 (namely the traceless Gaussian Unitary Ensemble random matrix) 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.
Piotr Sniady
Added 12 Dec 2010
Updated 12 Dec 2010
Type Journal
Year 2007
Where COMBINATORICS
Authors Piotr Sniady
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