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I am interested to know about random matrices and Wigner semi-circle law. Is there some easy-to-read recommendations. Possibly aimed at undergrads? non-technical stuff may help to just get a taste of whats going on

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  • $\begingroup$ How non-technical are we talking? $\endgroup$
    – scoopfaze
    Jul 19, 2019 at 18:13
  • $\begingroup$ like stuff published in American mathematical monthly journals $\endgroup$
    – Dreamer123
    Jul 19, 2019 at 18:17

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I started recently to study this field as well, and I have found the next documents (among the ones freely available on the Internet) the most relevant for my needs:

  • "Introduction to Random Matrices: Theory and Practice" from Giacomo Livan, Marcel Novaes, and Pierpaolo Vivo, available here: https://arxiv.org/pdf/1712.07903.pdf. This document aims at providing a good understanding of the basics concepts and equations of the random matrix theory in a detailled manner, with graphs and all. Moreover, MATLAB codes corresponding to the chapters are available online. I believe they can be easily translated into Python code for instance.

  • For some physics related issues, I found this short document (meant for undergrads) from Leticia Cugliandolo quite convincing: http://www.lpthe.jussieu.fr/~leticia/TEACHING/Master2017/random-matrices.pdf. In particular, the explanation about the origin of the Wigner surmise was clear to me.

Both are quite new (less than five years old), and I appreciated the tone adopted by the authors. I tried to read some other documents as well, like Metha's book on random matrices (actually not for beginners at all) and Alan Edelman's papers (available here: http://www-math.mit.edu/~edelman/), which were quite interesting but not as a first attempt.

I hope it helps.

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