On the Eigenvalues of Random Matrices
Copyright policy )On the Eigenvalues of Random Matrices
Let M be a random matrix chosen from Haar measure on the unitary group Un. Let Z = X + iY be a standard complex normal random variable with X and Y independent, mean 0 and variance ½ normal variables. We show that for j = 1, 2, …, Tr(Mj) are independent and distributed as √jZ asymptotically as n →∞. This result is used to study the set of eigenvalues of M. Similar results are given for the orthogonal and symplectic and symmetric groups.
Random matrices (algebraic aspects), unitary group, eigenvalue distribution, Gaussian distribution, Central limit and other weak theorems, compact groups, symplectic group, Inequalities involving eigenvalues and eigenvectors, random matrices, orthogonal group
Random matrices (algebraic aspects), unitary group, eigenvalue distribution, Gaussian distribution, Central limit and other weak theorems, compact groups, symplectic group, Inequalities involving eigenvalues and eigenvectors, random matrices, orthogonal group
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).217 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 1% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 1% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!