Concentration of Sums of Independent Random Variables
Abstract
This chapter introduces sub-Gaussian and sub-exponential distributions and develops basic concentration inequalities. We prove the Hoeffding, Chernoff, Bernstein, and Khintchine inequalities. Applications include robust mean estimation and analyzing degrees in random graphs. The exercises explore Mills ratio, small ball probabilities, Le Cam’s two-point method, the expander mixing lemma for random graphs, stochastic dominance, Orlicz norms, and the Bennett inequality.
Fields of Study & Subjects
Probability and Statistical Research
Statistical Methods and Inference
Point processes and geometric inequalities
Publication details
- Journal / source
- Cambridge University Press eBooks
- Pages
- 24–57
- Publication date
- 30 January 2026
- Document type
- Book chapter