 McDiarmid's inequality

If $X_1,\dots ,X_n$ are independent random variables and $f$ has bounded differences constants $c_i$, thenand the same bound holds for the lower tail.

McDiarmid's inequality is a result in probability theory that provides a bound on the concentration of a function that is composed of independent random variables. It is particularly useful for analyzing the behavior of functions that depend on a finite number of independent random variables and have bounded differences.