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It has been observed that the statistical distribution of the eigenvalues of random matrices possesses universal properties, independent of the probability law of the stochastic matrix. In this article we find the correlation functions of this distribution in two classes of random hermitian matrix models...
Summary: Random matrix theory has found many applications in physics, statistics and engineering since its inception. Although early developments were motivated by practical experimental problems, random matrices are now used in fields as diverse as Riemann hypothesis, stochastic differential equations, cond...
We study the fluctuation properties of transition intensities applying a recently proposed generalization of the random matrix theory, which is based on Beck and Cohen's superstatistics. We obtain an analytic expression for the distribution of the reduced transition probabilities that applies to systems...
We report some progress on the old problem of estimating the probability, Pn, that a random n × n ± 1-matrix is singular: Theorem. There is a positive co... J Kahn,János Komlós and Endre Szemerédi - 《Journal of the American Mathematical Society》 被引量: 277发表: 1995年 Sampling...
We define the row product of K matrices of size d by n as a matrix of size d^K by n, whose row are entry-wise products of rows of these matrices. This construction arises in certain computer science problems. We study the question, to which extent the spectral and geometric properties...
The method is based on the properties of random matrix eigenvalue density. First, we describe general ideas and support them with results of numerical simulations for basic periodic signals hidden in artificial stochastic noise. Then, the main effort is put to examine the strength of a new ...
These results strongly suggest that tools of graph theory, statistical physics, combinatorics and even number theory can be brought to bear on problems in control theory. 关键词: delay systems distributed control graph theory linear systems matrix algebra number theory random processes stochastic ...
In the 70’s, Robert May demonstrated that complexity creates instability in generic models of ecological networks having random interaction matrices A. Similar random matrix models have since been applied in many disciplines. Central to assessing stabil
The calculation of the hierarchy measure can be carried out based on repeated multiplications of an N by N transition matrix, making the method computationally very efficient and opens up the possibility for GPU based parallelisation. The other main advantage of our approach is that it can ...