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91.
On the distribution of the length of the longest increasing subsequence of random permutations 总被引:18,自引:0,他引:18
Jinho Baik Percy Deift Kurt Johansson 《Journal of the American Mathematical Society》1999,12(4):1119-1178
The authors consider the length, , of the longest increasing subsequence of a random permutation of numbers. The main result in this paper is a proof that the distribution function for , suitably centered and scaled, converges to the Tracy-Widom distribution of the largest eigenvalue of a random GUE matrix. The authors also prove convergence of moments. The proof is based on the steepest descent method for Riemann-Hilbert problems, introduced by Deift and Zhou in 1993 in the context of integrable systems. The applicability of the Riemann-Hilbert technique depends, in turn, on the determinantal formula of Gessel for the Poissonization of the distribution function of .
92.
Walter Trebels 《Proceedings of the American Mathematical Society》1999,127(10):2883-2887
Within the setting of abstract Cesàro-bounded Fourier series a -functional is introduced and characterized by the convergence behavior of some linear means. Applications are given within the framework of Jacobi, Laguerre and Hermite expansions. In particular, Ditzian's (1996) equivalence result in the setting of Legendre expansions is covered.
93.
Several new constructions for difference matrices are given. One classof constructions uses pairwise balanced designs to develop newdifference matrices over the additive group of GF (q). A second class of constructions gives difference matrices overgroups whose orders are not (necessarily) prime powers. 相似文献
94.
95.
A common method of fitting curves and surfaces to data is to minimize the sum of squares of the orthogonal distances from the data points to the curve or surface, a process known as orthogonal distance regression. Here we consider fitting geometrical objects to data when some orthogonal distances are not available. Methods based on the Gauss–Newton method are developed, analyzed and illustrated by examples.
AMS subject classification (2000) 65D10, 65K05. 相似文献
96.
97.
Wiebke S. Diestelkamp 《Designs, Codes and Cryptography》2004,33(3):187-197
An important question in the construction of orthogonal arrays is what the minimal size of an array is when all other parameters are fixed. In this paper, we will provide a generalization of an inequality developed by Bierbrauer for symmetric orthogonal arrays. We will utilize his algebraic approach to provide an analogous inequality for orthogonal arrays having mixed levels and show that the bound obtained in this fashion is often sharper than Raos bounds. We will also provide a new proof of Raos inequalities for arbitrary orthogonal arrays with mixed levels based on the same method. 相似文献
98.
H. Taşeli 《Journal of mathematical chemistry》2004,36(1):1-12
A new subclass of the Jacobi polynomials arising in the exact analytical solution of the one-dimensional Schrödinger equation with a trigonometric potential has been introduced. The polynomials which consist of a free parameter are not ultraspherical polynomials and have been simply named the
-polynomials since they are generated by a trigonometric Hamiltonian. In certain sense, it is shown that the
-polynomials can be regarded as a generalisation of the airfoil polynomials or the Chebyshev polynomials of the third kind. This paper is intended to discuss the basic properties of the polynomials so defined. 相似文献
99.
We derive an elementary formula for Janossy densities for determinantal point processes with a finite rank projection-type kernel. In particular, for =2 polynomial ensembles of random matrices we show that the Janossy densities on an interval I can be expressed in terms of the Christoffel–Darboux kernel for the orthogonal polynomials on the complement of I. 相似文献
100.
Let $\{P_n(x) \}_{n=0}^\infty$ be an orthogonal polynomial system
relative to a compactly supported measure. We find
characterizations for $\{P_n(x) \}_{n=0}^\infty$ to be a
Bochner--Krall orthogonal polynomial system, that is, $\{P_n(x)
\}_{n=0}^\infty$ are polynomial eigenfunctions of a linear
differential operator of finite order. In particular, we show that
$\{P_n(x) \}_{n=0}^\infty$ must be generalized Jacobi polynomials
which are orthogonal relative to a Jacobi weight plus two point
masses. 相似文献