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\title{Concentration Inequalities}
\author{Emin Karayel and Yong Kiam Tan$^*$}
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\def\thefootnote{*}\footnotetext{The authors contributed equally to this work.}\def\thefootnote{\arabic{footnote}}

\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, Bienaym\'e's Identity, Cantelli's Inequality,
the Efron-Stein Inequality, McDiarmid's Inequality, and the Paley-Zygmund
Inequality.}

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