This page is a high-level pointer to more specific concentration inequalities in various settings. See:
- light-tailed scalar concentration
- heavy-tailed scalar concentration
- martingale concentration
- multivariate concentration
- cdf concentration
- concentration in Banach spaces
- matrix inequalities
- concentration of functions
For notes related to techniques to achieve concentration, see:
- techniques for multivariate concentration
- exponential inequalities, which typically underlie the proofs of many concentration inequalities, and
- basic inequalities, which contains the building blocks for many concentration results (eg Markov’s inequality and the Chernoff method).
Note
Here we’re interested in measure-theoretic concentration, i.e., concentration in measure-theoretic probability spaces. This is what the vast majority of the statistics community means by concentration. But there is also a small literature on game-theoretic concentration inequalities.