## Basic concepts of random matrix theory

##### Abstract

It was Wigner that in the 1950’s first introduced the idea of modelling physical reality
with an ensemble of random matrices while studying the energy levels of heavy atomic
nuclei. Since then, the field of Random Matrix Theory has grown tremendously, with
applications ranging from fluctuations on the economic markets to M-theory. It is the
purpose of this thesis to discuss the basic concepts of Random Matrix Theory, using the
ensembles of random matrices originally introduced by Wigner, the Gaussian ensembles,
as a starting point. As Random Matrix Theory is classically concerned with the statistical
properties of levels sequences, we start with a brief introduction to the statistical analysis
of a level sequence before getting to the introduction of the Gaussian ensembles. With the
ensembles defined, we move on to the statistical properties that they predict. In the light
of these predictions, a few of the classical applications of Random Matrix Theory are
discussed, and as an example of some of the important concepts, the Anderson model of
localization is investigated in some detail.

##### Please cite this item using this persistent URL

http://hdl.handle.net/10019.1/1624##### Collections

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