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I read this fascinating article:

Unfortunately all the other papers I find googling are just not tangible to me :-(

Could anyone please point me to some material that bridges the gap from this popular science exposition to the hard core papers that seem to pile up in the Net?

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My guess is that random matrix theory is probably too new a subject for such material to exist. Have you tried the links in the Wikipedia article? – Qiaochu Yuan Aug 26 '10 at 20:34
@Qiaochu: Yes, I certainly have. I don't think it is that new - it reaches back half a century by now. But I agree that it lived a life in the shadows. – vonjd Aug 26 '10 at 20:54
I think this may be a good place to look: Patterns in Eigenvalues: The 70th Josiah Willard Gibbs Lecture. – Tom Stephens Aug 27 '10 at 16:19
@Tom: I've fixed the link. For reference, google's search results will give you a super-long url with lots of tracking information. It's usually better to click through the link and copy the address from your browser directly. – Larry Wang Aug 27 '10 at 17:12
up vote 6 down vote accepted

I like very much and I think that the exposition is very good and clear in the Deift's book: Orthogonal polynomials and random matrices: a Riemann-Hilbert approach.

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It is useful to have a link handy. Here is one to Amazon and Google Books. – Sasha Feb 9 '13 at 22:52

Random matrix theory is a diverse area; and different people prefer different introductions. One question is whether you're mostly interested in mathematical aspect or in applications in physics (and other areas). But I can recommend everything below.

Lecture notes

Topics in random matrix theory,
excellent lecture notes by Fields medallist Terence Tao

Introduction to the Random Matrix Theory: Gaussian Unitary Ensemble and Beyond,
lecture notes by Yan Fyodorov

Topics in random matrix theory
lectures mostly focused on QCD by Jac Verbaarschot


Random Matrices, by Madan Lal Mehta
canonical on the orthogonal polynomial approach

An Introduction to Random Matrices, by Greg Anderson, Alice Guionnet and Ofer Zeitouni

Overview of applications

The Oxford Handbook of Random Matrix Theory,
Editors: Gernot Akemann, Jinho Baik, Philippe Di Francesco.

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