In July I will be spending a week at Park City, being one of the mini-course lecturers in the Graduate Summer School component of the Park City Summer Session on random matrices. I have chosen to give some lectures on least singular values of random matrices, the circular law, and the Lindeberg exchange method in random matrix theory; this is a slightly different set of topics than I had initially advertised (which was instead about the Lindeberg exchange method and the local relaxation flow method), but after consulting with the other mini-course lecturers I felt that this would be a more complementary set of topics. I have uploaded an draft of my lecture notes (some portion of which is derived from my monograph on the subject); as always, comments and corrections are welcome.

*[Update, June 23: notes revised and reformatted to PCMI format. -T.]*

*[Update, Mar 19 2018: further revision. -T.]*

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9 June, 2017 at 8:06 am

AnonymousWill there be any videos posted online of the lectures?

12 June, 2017 at 6:23 pm

Tom CopelandNo connections to free probability theory?

15 June, 2017 at 5:41 pm

Nick CookConnections to free probability will be the focus of the lectures by Shlyakhtenko.

17 June, 2017 at 6:24 pm

Terry ChengWill there be any reports online?

21 June, 2017 at 1:24 am

DaniloEven though I do not understand anything, I want to watch the lecture online

29 June, 2017 at 9:14 am

JulianThis is probably a rather weird question, but what is the bibliography style and/or package used in the lecture notes? I find it visually pleasing and very useful with the MR-links and the page back-references

[pcmi.cls, see https://pcmi.ias.edu/author-info -T]9 July, 2017 at 10:10 pm

Keiji[correction]

1.1 The epsilon-net argument

– the proof of theorem 1.1.1(Upper bound for operator norm)

P(||Mx|| <= Cn^{1/2} / 2) < P(||Mx|| >= C n^{1/2} / 2) <= exp( -c C^{2} n / 4 + O(n) )

Thank you for uploading the lecture note.

[Thanks, this will be corrected in the next revision of the ms. -T.]