Physics In nuclear physics, random matrices were introduced by Eugene Wigner to model the nuclei of heavy atoms. Wigner postulated th… 展开
History
Random matrix theory first gained attention beyond mathematics literature in the context of nuclear physics. Experiments by Enrico Fermi and others demonstrated ev… 展开
Wikipedia
Gaussian Ensembles
The most-commonly studied random matrix distributions are the Gaussian ensembles: GOE, GUE and GSE. They are often denoted by their Dyson index, β = 1 for GOE, β = 2 for G… 展开
Wikipedia
Generalizations
Wigner matrices are random Hermitian matrices H n = ( H n ( i , j ) ) i , j = 1 n {\textstyle H_{n}=(H_{n}(i,j))_{i,j=1}^{n}} such that the entries Invariant matrix ensembles are r… 展开
Wikipedia
Correlation Functions
The joint probability density of the eigenvalues of n × n {\displaystyle n\times n} random Hermitian matrices M ∈ H n × n {\displaystyle M\in \mathbf {H} ^{n\times n}} , with partition fu… 展开
Wikipedia
Other Classes of Random Matrices
Wishart matrices Wishart matrices are n × n random matrices of the form H = X X*, where X is an n × m random matrix (m ≥ n) with independent entries, and X* i… 展开
网页Euclidean random matrix. Within mathematics, an N × N Euclidean random matrix  is defined with the help of an arbitrary deterministic function f ( r, r ′) and of N points { ri } …
网页Pages in category "Random matrices". The following 20 pages are in this category, out of 20 total. This list may not reflect recent changes . Random matrix. Wigner surmise.
网页So, what is a random matrix? Well, it is just a matrix whose elements are random variables. No big deal. So why all the fuss about it? Because they are extremely useful! Just think …
网页2011年9月23日 · Random Matrix Theory (frequently abbreviated as RMT) is an active research area of modern Mathematics with input from Mathematical and Theoretical …
网页The study of random matrices, and in particular the properties of their eigenval-ues, has emerged from the applications, first in data analysi s and later as statisti-cal models for …
网页RANDOM MATRIX THEORY AND THE SEMICIRCLE LAW ROGER VAN PESKI 0.1. Intro. 1 Classical random matrix theory over C, while now a full-edged eld of its own, arguably …