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random matrices
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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
G=3000000 M=2
G=3000000 M=2
G=3000000 M=2