The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.
A Brownian-Motion Model for the Eigenvalues of a Random Matrix
Abstract
A new type of Coulomb gas is defined, consisting of n point charges executing Brownian motions under the influence of their mutual electrostatic repulsions. It is proved that this gas gives an exact mathematical description of the behavior of the eigenvalues of an (n × n) Hermitian matrix, when the elements of the matrix execute independent Brownian motions without mutual interaction. By a suitable choice of initial conditions, the Brownian motion leads to an ensemble of random matrices which is a good statistical model for the Hamiltonian of a complex system possessing approximate conservation laws. The development with time of the Coulomb gas represents the statistical behavior of the eigenvalues of a complex system as the strength of conservation-destroying interactions is gradually increased. A ``virial theorem'' is proved for the Brownian-motion gas, and various properties of the stationary Coulomb gas are deduced as corollaries.
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Cites
On the Theory of the Brownian Motion
Uhlenbeck, G. E., & Ornstein, L. S. (1930) · Physical Review · doi:10.1103/physrev.36.823 · Cited by 4,482
Statistical Theory of the Energy Levels of Complex Systems. I
Dyson, F. J. (1962) · Journal of Mathematical Physics · doi:10.1063/1.1703773 · Cited by 2,266
Self-citationOn the Theory of the Brownian Motion II
Wang, M. C., & Uhlenbeck, G. E. (1945) · Reviews of Modern Physics · doi:10.1103/revmodphys.17.323 · Cited by 2,135
THE GENERALISED PRODUCT MOMENT DISTRIBUTION IN SAMPLES FROM A NORMAL MULTIVARIATE POPULATION
WISHART, J. (1928) · Biometrika · doi:10.1093/biomet/20a.1-2.32 · Cited by 1,207
The Threefold Way. Algebraic Structure of Symmetry Groups and Ensembles in Quantum Mechanics
Dyson, F. J. (1962) · Journal of Mathematical Physics · doi:10.1063/1.1703863 · Cited by 664
Self-citationNoise and stochastic processes
Wax, N. (1954) · Cited by 315
On the statistical properties of the level-spacings in nuclear spectra
Mehta, M. L. (1960) · Nuclear Physics · doi:10.1016/0029-5582(60)90413-2 · Cited by 186
Edwards, S. F., & Lenard, A. (1962) · Journal of Mathematical Physics · doi:10.1063/1.1724281 · Cited by 153
Cited by
Random-matrix theory of quantum transport
Beenakker, C. W. J. (1997) · Reviews of Modern Physics · doi:10.1103/revmodphys.69.731 · Cited by 2,551
Theory of Electronic States and Transport in Carbon Nanotubes
Ando, T. (2005) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.74.777 · Cited by 893
THE KARDAR–PARISI–ZHANG EQUATION AND UNIVERSALITY CLASS
CORWIN, I. (2012) · Random Matrices: Theory and Applications · doi:10.1142/s2010326311300014 · Cited by 759
Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
García-García, A. M., & Verbaarschot, J. J. M. (2016) · Physical Review D · doi:10.1103/physrevd.94.126010 · Cited by 325
The ergodic side of the many‐body localization transition
Luitz, D. J., & Lev, Y. B. (2017) · Annalen der Physik · doi:10.1002/andp.201600350 · Cited by 308
Metadata
- Authors
- Dyson, F. J.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1962-11-01
- Volume
- 3
- Issue
- 6
- Pages
- 1191-1198
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W1988076732
- Cited by
- 1,046
- References
- 8
- FWCI
- 4.83
- Type
- journal article
- Language
- en
- Open access
- closed
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