The Living Thing / Notebooks :

Random matrix theory

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 the more general general random matrix results.

I am mostly a consumer not a constructor f these theorems, so this page will remain forever sparse.

To read


Edelman, A., & Rao, N. R.(2005) Random matrix theory. Acta Numerica, 14, 233–297. DOI.
Krbálek, M., & Seba, P. (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.
Ormerod, P., & Mounfield, C. (2000) Random matrix theory and the failure of macro-economic forecasts. Physica A: Statistical Mechanics and Its Applications, 280(3–4), 497–504. DOI.
O’Rourke, S., Vu, V., & Wang, K. (2016) Eigenvectors of random matrices: A survey. Journal of Combinatorial Theory, Series A, 144(Supplement C), 361–442. DOI.
Racz, M. Z., & Richey, J. (2016) A smooth transition from Wishart to GOE. ArXiv:1611.05838 [Math, Stat].
Tropp, J. A.(2015) An Introduction to Matrix Concentration Inequalities. ArXiv:1501.01571 [Cs, Math, Stat].