Concentration inequality

In probability theory, concentration inequalities provide mathematical bounds on the probability of a random variable deviating from some value (typically, its expected value).

The law of large numbers of classical probability theory states that sums of independent random variables, under mild conditions, concentrate around their expectation with a high probability. Such sums are the most basic examples of random variables concentrated around their mean.

Concentration inequalities can be sorted according to how much information about the random variable is needed in order to use them.