Presentation Me Todos 2
16
-
Upload
andres-moreno -
Category
Documents
-
view
217 -
download
0
description
random matrices
Transcript of Presentation Me Todos 2
![Page 1: Presentation Me Todos 2](https://reader036.fdocuments.in/reader036/viewer/2022062408/563dbabb550346aa9aa78f8b/html5/thumbnails/1.jpg)
![Page 2: Presentation Me Todos 2](https://reader036.fdocuments.in/reader036/viewer/2022062408/563dbabb550346aa9aa78f8b/html5/thumbnails/2.jpg)
RandomMatrices
![Page 3: Presentation Me Todos 2](https://reader036.fdocuments.in/reader036/viewer/2022062408/563dbabb550346aa9aa78f8b/html5/thumbnails/3.jpg)
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?
![Page 4: Presentation Me Todos 2](https://reader036.fdocuments.in/reader036/viewer/2022062408/563dbabb550346aa9aa78f8b/html5/thumbnails/4.jpg)
Algorithm
*Random number with Gaussian Distribution
*build matrices *Compute eigenvalues
*ordering the eigenvalues and make the difference
![Page 5: Presentation Me Todos 2](https://reader036.fdocuments.in/reader036/viewer/2022062408/563dbabb550346aa9aa78f8b/html5/thumbnails/5.jpg)
Results G=3000000 M=2
![Page 6: Presentation Me Todos 2](https://reader036.fdocuments.in/reader036/viewer/2022062408/563dbabb550346aa9aa78f8b/html5/thumbnails/6.jpg)
Results G=3000000 M=2
![Page 7: Presentation Me Todos 2](https://reader036.fdocuments.in/reader036/viewer/2022062408/563dbabb550346aa9aa78f8b/html5/thumbnails/7.jpg)
Results G=3000000 M=2
![Page 8: Presentation Me Todos 2](https://reader036.fdocuments.in/reader036/viewer/2022062408/563dbabb550346aa9aa78f8b/html5/thumbnails/8.jpg)
Results G=20000 M=50
![Page 9: Presentation Me Todos 2](https://reader036.fdocuments.in/reader036/viewer/2022062408/563dbabb550346aa9aa78f8b/html5/thumbnails/9.jpg)
Results G=20000 M=50
![Page 10: Presentation Me Todos 2](https://reader036.fdocuments.in/reader036/viewer/2022062408/563dbabb550346aa9aa78f8b/html5/thumbnails/10.jpg)
Results G=3000000 M=2
![Page 11: Presentation Me Todos 2](https://reader036.fdocuments.in/reader036/viewer/2022062408/563dbabb550346aa9aa78f8b/html5/thumbnails/11.jpg)
Wigner distribution
![Page 12: Presentation Me Todos 2](https://reader036.fdocuments.in/reader036/viewer/2022062408/563dbabb550346aa9aa78f8b/html5/thumbnails/12.jpg)
conclusion
1
2
3
4.......
![Page 13: Presentation Me Todos 2](https://reader036.fdocuments.in/reader036/viewer/2022062408/563dbabb550346aa9aa78f8b/html5/thumbnails/13.jpg)
Reference
*Random Matrices
Madan Metha Centre Nucleaire de SaclayFrance
*Quantum Signature of ChaosFritz Haake University Essen
![Page 14: Presentation Me Todos 2](https://reader036.fdocuments.in/reader036/viewer/2022062408/563dbabb550346aa9aa78f8b/html5/thumbnails/14.jpg)
G=3000000 M=2
![Page 15: Presentation Me Todos 2](https://reader036.fdocuments.in/reader036/viewer/2022062408/563dbabb550346aa9aa78f8b/html5/thumbnails/15.jpg)
G=3000000 M=2
![Page 16: Presentation Me Todos 2](https://reader036.fdocuments.in/reader036/viewer/2022062408/563dbabb550346aa9aa78f8b/html5/thumbnails/16.jpg)
G=3000000 M=2