Concentration Inequalities

Emin Karayel, Yong Kiam Tan

Abstract: Concentration inequalities provide bounds on how a random variable (or a sum/composition of random variables) deviate from their expectation, usually based on moments/independence of the variables. The most important concentration inequalities (the Markov, Chebyshev, and Hoelder inequalities and the Chernoff bounds) are already part of HOL-Probability. This entry collects more advanced results, such as Bennett's/Bernstein's Inequality, Bienayme's Identity, Cantelli's Inequality, the Efron-Stein Inequality, McDiarmid's Inequality, and the Paley-Zygmund Inequality.