Averages of the Components of Random Unit Vectors
- 1 September 1972
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 13 (9) , 1399-1404
- https://doi.org/10.1063/1.1666153
Abstract
It is shown that a parametrization of the orthogonal and unitary groups due to Hurwitz can be used to evaluate averages of components of random unit vectors for those two spaces. Explicit results are given for moments which are general enough to include most cases of interest in applications.Keywords
This publication has 13 references indexed in Scilit:
- Matrices hermitiques aléatoires à partie imaginaire petiteIl Nuovo Cimento B (1971-1996), 1970
- Ensemble of Random Matrices with a Random BiasJournal of Mathematical Physics, 1968
- Distribution laws for the roots of a random antisymmetric hermitian matrixNuclear Physics A, 1968
- Perturbation of the statistical properties of nuclear states and transitions by interactions that are odd under time reversalNuclear Physics A, 1968
- Possibility of Detecting a Small Time-Reversal-Noninvariant Term in the Hamiltonian of a Complex System by Measurements of Energy-Level SpacingsPhysical Review Letters, 1967
- Invariance hypothesis and higher correlations of Hamiltonian matrix elementsNuclear Physics, 1964
- Reduced Width Amplitude Distributions for the Unitary EnsembleJournal of Mathematical Physics, 1963
- Invariance hypothesis and Hamiltonian matrix elements correlationsPhysics Letters, 1963
- Statistical Theory of the Energy Levels of Complex Systems. IJournal of Mathematical Physics, 1962
- Fluctuations of Nuclear Reaction WidthsPhysical Review B, 1956