Using transfer matrix method to solve 3D Ising model is generalized straightforwardly from 2D case. We follow the B.Kaufman's approach. No approximation is made except the largest eigenvalue cannot be identified. This problem comes from the fact that we follow the choice of directions of 2-dimensional rotations in direct product space of 2D Ising model such that all eigenvalue equations reduce ...

We investigate the statistical properties of the cross-correlation matrix between individual stocks traded in the Korean stock market using the random matrix theory (RMT) and observe how these affect the portfolio weights in the Markowitz portfolio theory. We find that the distribution of the cross-correlation matrix is positively skewed and changes over time. We find that the eigenvalue distri...

The decay rate of SIS epidemics on the complete graph KN is computed analytically, based on a new, algebraic method to compute the second largest eigenvalue of a stochastic three-diagonal matrix up to arbitrary precision. The latter problem has been addressed around 1950, mainly via the theory of orthogonal polynomials and probability theory. The accurate determination of the second largest eig...

We prove that the distribution function of the largest eigenvalue in the Gaussian Unitary Ensemble (GUE) in the edge scaling limit is expressible in terms of Painlevé II. Our goal is to concentrate on this important example of the connection between random matrix theory and integrable systems, and in so doing to introduce the newcomer to the subject as a whole. We also give sketches of the resu...

We present efficient numerical techniques for calculation of eigenvalue distributions of random matrices in the beta-ensembles. We compute histograms using direct simulations on very large matrices, by using tridiagonal matrices with appropriate simplifications. The distributions are also obtained by numerical solution of the Painlevé II and V equations with high accuracy. For the spacings we s...

Parity-time (PT) symmetric is not a necessary condition for achieving real spectrum and some studies about realizing spectra in non-PT-symmetric systems with arbitrary gain–loss profiles have been presented recently. By tuning the free parameters potentials, phase transition could also be induced. Above point, discrete complex eigenvalues bifurcate out from continuous interior of spectrum. In t...

We address the problem of computing the largest fraction of missing information for the EM algorithm and the worst linear function for data augmentation These are the largest eigenvalue and its associated eigenvector for the Jacobian of the EM operator at a maximum likelihood estimate which are important for assessing convergence in iterative simulation An estimate of the largest fraction of mi...

Abstract. In this paper, we study the perturbation bound for the spectral radius of an mthorder n-dimensional non-negative tensor A. The main contribution of this paper is to show that when A is perturbed to a non-negative tensor à by ∆A, the absolute difference between the spectral radii of A and à is bounded by the largest magnitude of the ratio of the i-th component of ∆Axm−1 and the i-th co...