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Eric S. Key 《Journal of Theoretical Probability》1990,3(3):477-488
Upper bounds for the maximal Lyapunov exponent,E, of a sequence of matrix-valued random variables are easy to come by asE is the infimum of a real-valued sequence. We shall show that under irreducibility conditions similar to those needed to prove the Perron-Frobenius theorem, one can find sequences which increase toE. As a byproduct of the proof we shall see that we may replace the matrix norm with the spectral radius when computingE in such cases. Finally, a sufficient condition for transience of random walk in a random environment is given. 相似文献
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关于HADAMARD不等式的注记 总被引:11,自引:0,他引:11
本文主要研究一类F-矩阵的性质,这类矩阵包含对称半正定矩阵,完全非负矩阵,τ矩阵和M-矩阵为其子类。我们不仅对F-矩阵改进了Hdamard不等式,而且证明对此类矩阵Hadamard不等式成立等式的充要条件是它的每条对角线,除主对角线外,都含有零元。 相似文献
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We present estimates on the small singular values of a class of matrices with independent Gaussian entries and inhomogeneous variance profile, satisfying a broad‐connectedness condition. Using these estimates and concentration of measure for the spectrum of Gaussian matrices with independent entries, we prove that for a large class of graphs satisfying an appropriate expansion property, the Barvinok–Godsil‐Gutman estimator for the permanent achieves sub‐exponential errors with high probability. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 48, 183–212, 2016 相似文献
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N. Balakrishnan Z. Govindarajulu K. Balasubramanian 《Annals of the Institute of Statistical Mathematics》1993,45(2):243-247
Govindarajulu expressed the moments of order statistics from a symmetric distribution in terms of those from its folded form. He derived these relations analytically by dividing the range of integration suitably into parts. In this paper, we establish these relations through probabilistic arguments which readily extend to the independent and non-identically distributed case. Results for random variables having arbitrary multivariate distributions are also derived.The first author would like to thank the Natural Sciences and Engineering Research Council of Canada for funding this research. 相似文献
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关于积和式差的一点注记 总被引:1,自引:0,他引:1
It is shown that for any two n×n complex valued matrices A, B the inequality |perA-perB|≤n‖A-B‖Fmax(‖A‖F,‖B‖F)n-1 or |perA-perB|≤‖A‖Fn ‖B‖Fn holds for where AH denotes the conjuagte transpose of the matrix A=(aij)n×n. 相似文献
7.
Vasileios A. Anagnostopoulos Yannis Sarantopoulos Andrew M. Tonge 《Mathematische Nachrichten》2012,285(1):47-55
If L is a continuous symmetric n‐linear form on a real or complex Hilbert space and $\widehat{L}$ is the associated continuous n‐homogeneous polynomial, then $\Vert L\Vert =\big \Vert \widehat{L}\big \Vert$. We give a simple proof of this well‐known result, which works for both real and complex Hilbert spaces, by using a classical inequality due to S. Bernstein for trigonometric polynomials. As an application, an open problem for the optimal lower bound of the norm of a homogeneous polynomial, which is a product of linear forms, is related to the so‐called permanent function of an n × n positive definite Hermitian matrix. We have also derived generalizations of Hardy‐Hilbert's inequality. 相似文献
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Boyd Geoff Micchelli Charles A. Strang Gilbert Zhou Ding-Xuan 《Advances in Computational Mathematics》2001,14(4):379-391
Every s×s matrix A yields a composition map acting on polynomials on R
s
. Specifically, for every polynomial p we define the mapping C
A
by the formula (C
A
p)(x):=p(Ax), xR
s
. For each nonnegative integer n, homogeneous polynomials of degree n form an invariant subspace for C
A
. We let A
(n) be the matrix representation of C
A
relative to the monomial basis and call A
(n) a binomial matrix. This paper studies the asymptotic behavior of A
(n) as n. The special case of 2×2 matrices A with the property that A
2=I corresponds to discrete Taylor series and motivated our original interest in binomial matrices. 相似文献
9.
Let G be a connected k–regular bipartite graph with bipartition V(G) = X ∪ Y and adjacency matrix A. We say G is det‐extremal if per (A) = |det(A)|. Det–extremal k–regular bipartite graphs exist only for k = 2 or 3. McCuaig has characterized the det‐extremal 3‐connected cubic bipartite graphs. We extend McCuaig's result by determining the structure of det‐extremal cubic bipartite graphs of connectivity two. We use our results to determine which numbers can occur as orders of det‐extremal connected cubic bipartite graphs, thus solving a problem due to H. Gropp. © 2003 Wiley Periodicals, Inc. J Graph Theory 44: 50–64, 2003 相似文献
10.
D. Berend 《Discrete Mathematics》2018,341(11):3241-3248
We provide an upper bound on the number of Sudoku squares, and explain intuitively why there is reason to believe that the bound is tight up to a multiplicative factor of a much smaller order of magnitude. A similar bound is established for Sudoku squares with rectangular regions. 相似文献
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