There is few posts on MO that asked about reference on this topic, and I found some difficulty during the process of getting myself into the subject so here is the question.
I really want to hear from someone who is familiar with this wonderful field of random matrices.
1 I would like to know a self-study material on the subject of random matrix theory, which should be more advanced than [Tao]. I did read into [Tao]'s "Related article" part but found it focus on dynamics instead of a general interest like the content of [Mehta] covered.
2 About the classic in the field [Mehta], I am confused about its editions since some probabilist said the 2nd edition is better than the third one while 3rd edition is almost 200 pages of more than the 2nd edition.
Since I have not started to read it yet, I would like to know which edition of [Mehta] is better to start (as a newcomer to the subject) with, and what is the difference between these two editions(besides those newly added references Mehta mentioned in the 3rd edition's preface, which is not very informative to me…)?
3 Maybe this should be another post, but how much (statistical) mechanics should I know if I want to read [Deift&Gioev] in order to understand it better? Since my basic interest is in the mathematical side, is there any good-and-short introductory paper providing an overview about the subject of statistical mechanics?
4 Lastly, I would really like to know if there is some must-read or introductory paper on the subject of random matrices. (Besides [Tao].)
And a roadmap of learning this subject, if possible, will be greatly appreciated.
Reference
[Mehta]Mehta, Madan Lal. Random matrices. Vol. 142. Academic press, 2004.
[Deift&Gioev]Deift, Percy, and Dimitri Gioev. Random matrix theory: invariant ensembles and universality. Vol. 18. American Mathematical Soc., 2009.
[Tao]Tao, Terence. Topics in random matrix theory. Vol. 132. Providence, RI: American Mathematical Society, 2012.
https://terrytao.files.wordpress.com/2011/02/matrix-book.pdf
Best Answer
The
Oxford handbook of random matrix theory(Oxford University Press, 2011), edited by G. Akemann, J. Baik, P. Di Francesco, is an excellent reference, which covers a wide variety of properties and applications of random matrices (this is a very diverse subject). It is not a textbook, but a collection of introductory papers by different authors, which are well written and have many references that you can follow up.I must also mention the book
Log-gases and random matrices, by Peter Forrester (Princeton University Press), which is probably close to what you want (advanced, comprehensive, pedagogical).