Category: Random matrices

Complex Wishart distribution
In statistics, the complex Wishart distribution is a complex version of the Wishart distribution. It is the distribution of times the sample Hermitian covariance matrix of zero-mean independent Gaussi
Tracy–Widom distribution
The Tracy–Widom distribution is a probability distribution from random matrix theory introduced by Craig Tracy and Harold Widom . It is the distribution of the normalized largest eigenvalue of a rando
Isotropic position
In the fields of machine learning, the theory of computation, and random matrix theory, a probability distribution over vectors is said to be in isotropic position if its covariance matrix is equal to
Matrix normal distribution
In statistics, the matrix normal distribution or matrix Gaussian distribution is a probability distribution that is a generalization of the multivariate normal distribution to matrix-valued random var
Matrix t-distribution
In statistics, the matrix t-distribution (or matrix variate t-distribution) is the generalization of the multivariate t-distribution from vectors to matrices. The matrix t-distribution shares the same
Wigner surmise
In mathematical physics, the Wigner surmise is a statement about the probability distribution of the spaces between points in the spectra of nuclei of heavy atoms, which have many degrees of freedom,
Circular law
In probability theory, more specifically the study of random matrices, the circular law concerns the distribution of eigenvalues of an n × n random matrix with independent and identically distributed
Water retention on random surfaces
Water retention on random surfaces is the simulation of catching of water in ponds on a surface of cells of various heights on a regular array such as a square lattice, where water is rained down on e
Matrix variate beta distribution
In statistics, the matrix variate beta distribution is a generalization of the beta distribution. If is a positive definite matrix with a matrix variate beta distribution, and are real parameters, we
Circular ensemble
In the theory of random matrices, the circular ensembles are measures on spaces of unitary matrices introduced by Freeman Dyson as modifications of the Gaussian matrix ensembles. The three main exampl
Matrix gamma distribution
In statistics, a matrix gamma distribution is a generalization of the gamma distribution to positive-definite matrices. It is a more general version of the Wishart distribution, and is used similarly,
Random matrix
In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all elements are random variables. Many important properties of ph
Marchenko–Pastur distribution
In the mathematical theory of random matrices, the Marchenko–Pastur distribution, or Marchenko–Pastur law, describes the asymptotic behavior of singular values of large rectangular random matrices. Th
Inverse matrix gamma distribution
In statistics, the inverse matrix gamma distribution is a generalization of the inverse gamma distribution to positive-definite matrices. It is a more general version of the inverse Wishart distributi
Weingarten function
In mathematics, Weingarten functions are rational functions indexed by partitions of integers that can be used to calculate integrals of products of matrix coefficients over classical groups. They wer
Euclidean random matrix
Within mathematics, an N×N Euclidean random matrix Â is defined with the help of an arbitrary deterministic function f(r, r′) and of N points {ri} randomly distributed in a region V of d-dimensional E
Lewandowski-Kurowicka-Joe distribution
In probability theory and Bayesian statistics, the Lewandowski-Kurowicka-Joe distribution, often referred to as the LKJ distribution, is a continuous probability distribution for a symmetric matrix. I
Wishart distribution
In statistics, the Wishart distribution is a generalization to multiple dimensions of the gamma distribution. It is named in honor of John Wishart, who first formulated the distribution in 1928. It is
Montgomery's pair correlation conjecture
In mathematics, Montgomery's pair correlation conjecture is a conjecture made by Hugh Montgomery that the pair correlation between pairs of zeros of the Riemann zeta function (normalized to have unit