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.
Djalil Chafaï, Around the circular law : an update.
This post gathers comments and updates about the survey Around the circular law (2012).
- Bibliography and history at Scholarpedia
- 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.
- 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 macro-economic 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