# A Brownian‐Motion Model for the Eigenvalues of a Random Matrix

@article{Dyson1962ABM, title={A Brownian‐Motion Model for the Eigenvalues of a Random Matrix}, author={Freeman J. Dyson}, journal={Journal of Mathematical Physics}, year={1962}, volume={3}, pages={1191-1198} }

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…

## 872 Citations

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