Proof methods in random matrix theory

Universality in Random Matrix Theory

which is the Central Limit Theorem. In principle, all the random variables X1, X2, · · · , XN can be of order 1, hence SN ∼ 1 as well, but the probability of having such a rare event is incredibly small. We can even estimate the bound on the probability for the rare event from the large deviation principle. A similar phenomenon happens when we form a large matrix from i.i.d. random variables an...

Developments in Random Matrix Theory

In this preface to the Journal of Physics A, Special Edition on Random Matrix Theory, we give a review of the main historical developments of random matrix theory. A short summary of the papers that appear in this special edition is also given.

Random Matrix Theory

Random matrix theory is usually taught as a sequence of several graduate courses; we have 16 lectures, so we will give a very brief introduction. Some relevant books for the course: • G. Anderson, A. Guionnet, O. Zeitouni. An introduction to random matrices. [1] • A. Guionnet. Large random matrices: lectures on macroscopic asymptotics. • M. L. Mehta. Random matrices. The study of random matrice...

Random matrix theory

Random matrix theory is now a big subject with applications in many disciplines of science, engineering and finance. This article is a survey specifically oriented towards the needs and interests of a numerical analyst. This survey includes some original material not found anywhere else. We include the important mathematics which is a very modern development, as well as the computational softwa...

Random Matrix Theory