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).

- 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.

## 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 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