Wigner Random Matrix Ensembles, symmetry classes, semicircle law, concentration of measure techniques, Circular Random Matrix Ensembles, numerical experiments with random matrices, connections to graph enumeration and free probability. Prerequisites: undergraduate linear algebra, integration and measure.
The students will become familiar with the principal ensembles of random matrices, the eigenvalue statistics on different scales and methods of their derivation. Students will be able to generate random matrices numerically to obtain experimental confirmation of the observed mathematical laws.
Dr Michael Anshelevich, Blocker 533d.
Email: manshel AT math.tamu.edu
Dr Gregory Berkolaiko, Blocker 625c. Email: berko AT math.tamu.edu
3 credits
Blocker 628, TR 12:45-2pm.
TBA
5 homework assignments.
The following grade breakdown will be used:
| Grade | Percentage |
| A | 90% and more |
| B | 80% and more |
| C | 70% and more |
| D | 60% and more |
| F | less than 60% |
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