How can I learn Random Matrix theory as a first year undergraduate student?

Question

I have finished Strang's Introduction to Linear Algebra twice and Axler's Linear Algebra Done Right and also I have finished MIT OCW 6.041 Probability Course,I am very interested in Random Matrix Theory,I think that might be good for Deep Learning and Machine Learning, so I want to ask question How can I learn Random Matrix theory and is my mathematical background sufficient to understand RMT, also I know Calculus 1-2-3 and Differential Equations.

Thanks for responses.

Answer 1

Okan, lisansin ilk yilinda random matrix theory ogrenmek istemen vizyon sahibi oldugunu gösteriyor ;) Hangi okuldansin?

Leaving this aside, this would be my response:

• First, I'd say that the probability you'll need for random matrix theory (RMT) would require fair amount of concentration inequalities. Be sure to have completely mastered those (starting from basic Markov-Chebyshev bound to Chernoff, Azuma, McDiarmid type inequalities). While they may not be directly applicable, the way to develop these inequalities is quite universal.
• Do read stuff such as variational characterization of eigenvalues (e.g. Courant-Fischer minimax principle). For this type of linear algebra background, you'd need slightly more than Axler and Strang. One good book is Matrix Analysis by Horn and Johnson.
• You need a bit more advanced stuff, again on probability line. For instance, standard courses does not cover very much stuff on Gaussians. The stuff including how to handle Gaussian (and in general exponential tails), Gaussian integration by parts, maximum of Gaussian, all revolve around similar themes, but you need to learn them.
• You can start reading notes of Roman Vershynin here: https://arxiv.org/abs/1011.3027 Funnily, as I write this, I do have the note in front of me now, to be used in my research.