The study of "high dimensional" probability deals with the behaviour of random vectors, random matrices, random subspaces and objects used to quantify uncertainty in large dimension. Based on ideas from probability, analysis and geometry, high dimensional probability lends itself to applications in mathematics, statistics, theoretical computing, signal processing, optimization, etc.
1 Concentration inequalities: from classical results (Hoeffding, Chernoff, ...) to modern developments (Bernstein matrix inequality)
2 Methods dealing with stochastic processes :
 Inequality (Slepian, Sudakov, ...)
 Chaining (entropic and generic)
 VapnikChervonenkis classes.
3 Illustrations
 covariance estimation,
 clustering,
 networks,
 Semidefined programming,
 compressed sensing
 parsimonious regression
 ...
Références :

HighDimensional Probability: An Introduction with Applications in Data Science (Cambridge Series in Statistical and Probabilistic Mathematics) Sep 30, 2018 by Roman Vershynin
 van Handel, R. (2014).
Probability in high dimension. PRINCETON UNIV NJ.
Boucheron, S., Lugosi, G., & Massart, P. (2013).
Concentration inequalities: A nonasymptotic theory of independence. Oxford university press.