RandomMatrices

Consider a large matrix whose elements are random variables with given probability laws. Then what

can say about the probabilities of a few of its eigenvalues or a few of its

eigenvectors?

Algorithm

*Random number with Gaussian Distribution

*build matrices *Compute eigenvalues

*ordering the eigenvalues and make the difference

Results G=3000000 M=2

Results G=3000000 M=2

Results G=3000000 M=2

Results G=20000 M=50

Results G=20000 M=50

Results G=3000000 M=2

Wigner distribution

conclusion

1

2

3

4.......

Reference

*Random Matrices

Madan Metha Centre Nucleaire de SaclayFrance

*Quantum Signature of ChaosFritz Haake University Essen