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On the distribution of the length of the longest increasing subsequence of random permutations
 J. Amer. Math. Soc
, 1999
"... Let SN be the group of permutations of 1, 2,...,N. If π ∈ SN,wesaythat π(i1),...,π(ik) is an increasing subsequence in π if i1 <i2 <·· · <ikand π(i1) < π(i2) < ···<π(ik). Let lN (π) be the length of the longest increasing subsequence. For example, if N =5andπis the permutation 5 1 ..."
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Cited by 508 (32 self)
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Let SN be the group of permutations of 1, 2,...,N. If π ∈ SN,wesaythat π(i1),...,π(ik) is an increasing subsequence in π if i1 <i2 <·· · <ikand π(i1) < π(i2) < ···<π(ik). Let lN (π) be the length of the longest increasing subsequence. For example, if N =5andπis the permutation 5 1
RANDOM PERMUTATIONS AND BERNOULLI SEQUENCES
"... ABSTRACT. — The socalled first fundamental transformation provides a natural combinatorial link between statistics involving cycle lengths of random permutations and statistics dealing with runs on Bernoulli sequences. 1. ..."
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ABSTRACT. — The socalled first fundamental transformation provides a natural combinatorial link between statistics involving cycle lengths of random permutations and statistics dealing with runs on Bernoulli sequences. 1.
RANDOM PERMUTATIONS WITH CYCLE WEIGHTS
, 908
"... Abstract. We study the distribution of cycle lengths in models of nonuniform random permutations with cycle weights. We identify several regimes. Depending on the weights, the length of typical cycles grows like the total number n of elements, or a fraction of n, or a logarithmic power of n. ..."
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Cited by 17 (4 self)
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Abstract. We study the distribution of cycle lengths in models of nonuniform random permutations with cycle weights. We identify several regimes. Depending on the weights, the length of typical cycles grows like the total number n of elements, or a fraction of n, or a logarithmic power of n.
Random matrices and random permutations
 Internat. Math. Res. Notices
, 2000
"... We prove the conjecture of Baik, Deift, and Johansson which says that with respect to the Plancherel measure on the set of partitions λ of n, the rows λ1,λ2,λ3,... of λ behave, suitably scaled, like the 1st, 2nd, 3rd, and so on eigenvalues of a Gaussian random Hermitian matrix as n → ∞. Our proof is ..."
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Cited by 77 (7 self)
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We prove the conjecture of Baik, Deift, and Johansson which says that with respect to the Plancherel measure on the set of partitions λ of n, the rows λ1,λ2,λ3,... of λ behave, suitably scaled, like the 1st, 2nd, 3rd, and so on eigenvalues of a Gaussian random Hermitian matrix as n → ∞. Our proof
Random walks and random permutations
, 1999
"... A connection is made between the random turns model of vicious walkers and random permutations indexed by their increasing subsequences. Consequently the scaled distribution of the maximum displacements in a particular asymmeteric version of the model can be determined to be the same as the scaled d ..."
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A connection is made between the random turns model of vicious walkers and random permutations indexed by their increasing subsequences. Consequently the scaled distribution of the maximum displacements in a particular asymmeteric version of the model can be determined to be the same as the scaled
Subsequences of Random Permutations
"... We offer an easy proof that the average length of an increasing subsequence in a random permutation of { 1, 2,..., n} is Θ ( √ n). The proof uses the tool from theoretical computer science known as Kolmogorov complexity and the combinatorial structure known as a Young tableau. Introduction. In Knut ..."
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We offer an easy proof that the average length of an increasing subsequence in a random permutation of { 1, 2,..., n} is Θ ( √ n). The proof uses the tool from theoretical computer science known as Kolmogorov complexity and the combinatorial structure known as a Young tableau. Introduction
of a random permutation matrix
, 2000
"... random matrix theory, characteristic polynomial permutations, central limit theorem We establish a central limit theorem for the logarithm of the characteristic polynomial of a random permutation matrix. With this result we can obtain a central limit theorem for the counting function for the eigenva ..."
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random matrix theory, characteristic polynomial permutations, central limit theorem We establish a central limit theorem for the logarithm of the characteristic polynomial of a random permutation matrix. With this result we can obtain a central limit theorem for the counting function
Exact testing with random permutations
, 2014
"... The way in which random permutations have been used in various permutationbased methods leads to anticonservativeness, especially in multiple testing contexts. Problems arise in particular for Westfall and Young’s maxT method, a more recent method by Meinshausen and a global test that we introduce ..."
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The way in which random permutations have been used in various permutationbased methods leads to anticonservativeness, especially in multiple testing contexts. Problems arise in particular for Westfall and Young’s maxT method, a more recent method by Meinshausen and a global test that we
Fragmenting random permutations
, 2007
"... Problem 1.5.7 from Pitman’s SaintFlour lecture notes [9]: Does there exist for each n a Pnvalued fragmentation process (Πn,k, 1 ≤ k ≤ n) such that Πn,k is distributed like the partition generated by cycles of a uniform random permutation of [n] conditioned to have k cycles? We show that the answer ..."
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Problem 1.5.7 from Pitman’s SaintFlour lecture notes [9]: Does there exist for each n a Pnvalued fragmentation process (Πn,k, 1 ≤ k ≤ n) such that Πn,k is distributed like the partition generated by cycles of a uniform random permutation of [n] conditioned to have k cycles? We show
Results 1  10
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159,857