In mesoscopic systems, where inelastic mean free path for electrons is larger than the system size, such fluctuations originate in disorder and/or chaotic scattering. In both cases, the complex Hamiltonian dynamics can be simulated in terms of random-matrix models having the correct symmetry ...
Theorem 1 below shows that, with high probability, the eigenvalues of many matrices under discussion are simple and the coordinates of all eigenvectors are non-zero. Theorem 1 ([2]). Let W be an n×n Wigner matrix with atom variables ξ,ζ. If ξ is non-degenerate, then, for every ...
We derive an exact formula for the stochastic evolution of the characteristic determinant of a class of deformed Wishart matrices following from a chiral random matrix model of QCD at finite chemical potential. In the WKB approximation, the characteristic determinant describes a sharp droplet of ...
We review the development of random-matrix theory (RMT) during the last fifteen years. We emphasize both the theoretical aspects, and the application of the theory to a number of fields. These comprise chaotic and disordered systems, the localization problem, many-body quantum systems, the Caloge...
random matrix theory:随机矩阵理论 热度: random matrices and number theory:随机矩阵与数理论 热度: Matrix Functions Theory and Algorithms:矩阵函数理论和算法 热度: The Oxford Handbook of Random Matrix Theory Editors Gemot Akemann, Jinho Balk and ...
Large-dimensional random matrix theory and its applications in deep learning and wireless communications Jungang Ge, Ying-Chang Liang, Zhidong Bai, and Guangming Pan Vol. 10, No. 04 On random matrices arising in deep neural networks: General I.I.D. case ...
random matrix theory:随机矩阵理论 下载积分: 3000 内容提示: Acta Numerica (2005), pp. 1–65 c ? Cambridge University Press, 2005DOI: 10.1017/S0962492904000236 Printed in the United KingdomRandom matrix theoryAlan EdelmanDepartment of Mathematics,Massachusetts Institute of Technology,Cambridge, MA ...
马尔可夫性保证了一个马尔可夫链能被唯一的一个单步转移矩阵 (transition matrix) 所刻画,其形如: \mathbf{P}=\begin{pmatrix}P_{0,0} & P_{0,1} & \cdots & P_{0,j} & \cdots \\P_{1,0} & P_{1,1} & \cdots & P_{1,j} & \cdots \\\vdots & \vdots & \ddots & \v...
Example 37-6. Transforming the Wallace Pool Using a Defined Number of Passes and a Walsh-Hadamard Matrix on Each Set of Values This uses a defined number of passes and a Walsh-Hadamard matrix on each set of values. The size of the block to execute a matrix on can be varied ...
The joint pdf of Gaussian random variables is determined by the vector of means and a covariance matrix. For a Gaussian random process X(t), the joint pdf of two random variables resulting from sampling X(t), i.e., X(t1), X(t2), is completely specified by the set of means mX(t)...