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. Particular emphasis will be given to computing correlations of eigenvalues of ensembles of unitary and Hermitian matrices. It is a remarkable fact that predictions made using random matrix theory have turned out to be accurate in a wide range of fields: statistical mechanics, quantum chaos, nuclear physics, number theory, combinatorics, wireless telecommunications and structural dynamics, to name only few examples. 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. Unit availability varies depending on both staffing, student choice and timetablingīy the end of the unit you will master some of the most important mathematical techniques used in random matrix theory and have an understanding of how these are relevant in various areas of mathematics, physics, engineering and probability. Please note: It is possible that the information shown for futureĪcademic years may change due to developments in the relevant academic field.
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