Many dimensions plus linear algebra plus probability equals Random Matrix Theory.
Turns out to pop up in a lot of linear systems and adjacency graphs and induce some elegant results, and be useful where linear algebra is (“the whole modern world”) therefore super trendy.
I mostly encounter this though matrix concentration, which you can infer using general random matrix results.
I am a consumer not a constructor of these theorems, so this page will remain forever sparse.
To read

Djalil Chafaï, Around the circular law : an update.
This post gathers comments and updates about the survey Around the circular law (2012).
 Anderson, Guionnet and Zeitounni's course
 Tao's course and blog posts
 OrVW16 reviews results on eigenvectors of random matrices, not just eigenvalues, which is nice.
Refs
 RaRi16: (2016) A smooth transition from Wishart to GOE. ArXiv:1611.05838 [Math, Stat].
 Trop15: (2015) An Introduction to Matrix Concentration Inequalities. ArXiv:1501.01571 [Cs, Math, Stat].
 BoCh12: (2012) Around the circular law. Probability Surveys, 9(0), 1–89. DOI
 OrVW16: (2016) Eigenvectors of random matrices: A survey. Journal of Combinatorial Theory, Series A, 144(Supplement C), 361–442. DOI
 EdRa05: (2005) Random matrix theory. Acta Numerica, 14, 233–297. DOI
 OrMo00: (2000) Random matrix theory and the failure of macroeconomic forecasts. Physica A: Statistical Mechanics and Its Applications, 280(3–4), 497–504. DOI
 KrSe00: (2000) The statistical properties of the city transport in Cuernavaca (Mexico) and random matrix ensembles. Journal of Physics A: Mathematical and General, 33(26), L229–L234. DOI