| Unit name | Random Theory Matrix |
|---|---|
| Unit code | MATH33700 |
| Credit points | 10 |
| Level of study | H/6 |
| Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
| Unit director | Professor. Mezzadri |
| Open unit status | Not open |
| Pre-requisites |
Linear algebra 2 and Calculus 2. |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Random matrices are often used to study the statistical properties of systems whose detailed mathematical description is either not known or too complicated to allow any kind of successful approach. It is a remarkable fact that predictions made using random matrix theory have turned out to be accurate in a wide range of fields: statisitcal mechanics, quantum chaos, nuclear physics, number theory and combinatorics, to name only a few examples. Particular emphasis will be given to computing correlation of eigenvalues of ensembles of unitary and Hermition matrices. Different ensembles have distinct invariance properties, which in the applications are used to model systems whose physical or mathematical behaviour depends only on their symmetries. In most cases the dimension of the matrices will be treated as a large asymptotic parameter. In addition we will develop several techniques to compute certain types of multiple integrals. For each topic several examples of applications to differnt branches of mathematics and physics will be given. The course will appeal to students in applied and pure mathematics as well as in statistics.
