# Random Matrices

@inproceedings{Stephanov2005RandomM, title={Random Matrices}, author={Mikhail A. Stephanov and Jacobus J. M. Verbaarschot and Tilo Wettig}, year={2005} }

. We review elementary properties of random matrices and discuss widely used mathematical methods for both hermitian and nonhermitian random matrix ensembles. Applications to a wide range of physics problems are summarized. This paper originally appeared as an article in the Wiley Encyclopedia of Electrical and Electronics Engineering.

## 3,906 Citations

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Author(s): Soshnikov, Alexander | Abstract: The paper studies the spectral properties of large Wigner, band and sample covariance random matrices with heavy tails of the marginal distributions of…

## References

SHOWING 1-9 OF 9 REFERENCES

### Statistical Theory of Spectra: Fluctuations

- 1965

### Sciences Research Institute 1000 Centennial Drive, Berkeley CA 94720-5070 510.642.8609 @BULLET FAX 510

- Sciences Research Institute 1000 Centennial Drive, Berkeley CA 94720-5070 510.642.8609 @BULLET FAX 510

### Weidenmüller, and M.R

- Zirnb auer, Phys. Rep
- 1985

### A: Math

- Gen. 17 (1985)

### Mathematical Sciences Institutes Reception

- Mathematical Sciences Institutes Reception

### in Nuclear data for science and technology , ed

- K.H. Böchhoff (Reidel, Dordrecht,
- 1983

### Before the Gibbs Lecture) See old friends, find out what's going on, and have a bite at a reception organized by MSRI, featuring: Centre de

- Center for Discrete Mathematics and Theoretical Computer Science (DIMACS, New Jersey), Fields Institute (FI, Toronto), Institute for Mathematics and Its Applications (IMA, Minneapolis), Institute for Pure and Applied Mathematics (IPAM, Los Angeles), Mathematical Sciences Research Institute (MSRI, Be
- 2000

### P hys

- Rev. Lett. 60 (1988)
- 1895

### aarschot, and T

- Wettig, Phys. Rev. Lett. 80 (1998)