mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all of its entries are sampled randomly from a probability...

covariance between each pair of elements of a given random vector. Intuitively, the covariance matrix generalizes the notion of variance to multiple dimensions...

and measurements of a quantum circuit. The idea is similar to that of random matrix theory which is to use the QRC to obtain almost exact results of non-integrable...

of aggregate random variables, e.g. a random matrix, random tree, random sequence, stochastic process, etc. Formally, a multivariate random variable is...

the distribution in 1928. Other names include Wishart ensemble (in random matrix theory, probability distributions over matrices are usually called "ensembles")...

an N×N Euclidean random matrix  is defined with the help of an arbitrary deterministic function f(r, r′) and of N points {ri} randomly distributed in a...

In mathematics, a matrix (pl.: matrices) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows...

theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix or discrete Laplacian, is a matrix representation of a...

distribution to matrix-valued random variables. The probability density function for the random matrix X (n × p) that follows the matrix normal distribution...

are positive. The matrix J {\displaystyle J} is also known as the community matrix. May supposed that the Jacobian was a random matrix whose off-diagonal...

cross-correlation matrix of two random vectors is a matrix containing as elements the cross-correlations of all pairs of elements of the random vectors. The...

functions of a matrix argument have applications in random matrix theory. For example, the distributions of the extreme eigenvalues of random matrices are...

general class of random matrix products, the norm grows as λn, where n is the number of factors. Their results apply to a broad class of random sequence generating...

statistics, information and communication sciences with a special focus on random matrix theory and learning algorithms. In the AI field, he is known for his...

is a British mathematician at the University of Bristol working in random matrix theory and quantum chaos. Snaith was educated at the University of Bristol...

generated free groups have the same elementary theory. Later connections to random matrix theory, combinatorics, representations of symmetric groups, large deviations...

normal complex random vectors that are circularly symmetric are of particular interest because they are fully specified by the covariance matrix Γ {\displaystyle...

subspace. Random projection is computationally simple: form the random matrix "R" and project the d × N {\displaystyle d\times N} data matrix X onto K...

a cross-covariance matrix is a matrix whose element in the i, j position is the covariance between the i-th element of a random vector and j-th element...

In statistics, sometimes the covariance matrix of a multivariate random variable is not known but has to be estimated. Estimation of covariance matrices...

ISBN 978-1108120494. Asymptotic safety in quantum gravity Cavity method Euclidean random matrix Parisi–Sourlas stochastic quantization procedure p-adic quantum mechanics...

e.g. a random matrix, random tree, random sequence, random process, etc. A random matrix is a matrix-valued random element. Many important properties...

Random element Random field Random function Random graph Random matrix Random measure Random multinomial logit Random naive Bayes Random permutation statistics...

In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. One way to express...

covariance matrix is called the precision matrix, denoted by Q = Σ − 1 {\displaystyle {\boldsymbol {Q}}={\boldsymbol {\Sigma }}^{-1}} . A real random vector...

numerical linear algebra, computational science, parallel computing, and random matrix theory. He is one of the creators of the technical programming language...

is a generalization of the population growth rate to when a Leslie matrix has random elements which may be correlated. When characterizing the disorder...

Correlation matrix — a symmetric n×n matrix, formed by the pairwise correlation coefficients of several random variables. Covariance matrix — a symmetric...

and uniformly bounded random variables. In the matrix setting, the analogous theorem concerns a sum of positive-semidefinite random matrices subjected to...

random variables with finite second moments, its auto-covariance matrix (also known as the variance–covariance matrix or simply the covariance matrix)...