  Let $Y$ be a nonnegative random variable with mean $\mu$ and finite positive
variance $\sigma^2$, and let $Y^s$, defined on the same space as $Y$, have the
$Y$ size biased distribution, that is, the distribution characterized by
E[Yf(Y)]=\mu E f(Y^s) for all functions $f$ for which these expectations exist.
Under a variety of conditions on the coupling of Y and $Y^s$, including
combinations of boundedness and monotonicity, concentration of measure
inequalities hold. Examples include the number of relatively ordered
subsequences of a random permutation, sliding window statistics including the
number of m-runs in a sequence of coin tosses, the number of local maximum of a
random function on a lattice, the number of urns containing exactly one ball in
an urn allocation model, the volume covered by the union of $n$ balls placed
uniformly over a volume n subset of d dimensional Euclidean space, the number
of bulbs switched on at the terminal time in the so called lightbulb process,
and the infinitely divisible and compound Poisson distributions that satisfy a
bounded moment generating function condition.
