  Talagrand's inequality for independent Bernoulli random variables is extended
to many interacting particle systems (IPS). The main assumption is that the IPS
satisfies a log-Sobolev inequality. In this context it is also shown that a
slightly stronger version of Talagrand's inequality is equivalent to a
log-Sobolev inequality.
  Additionally we also look at a common application, the relation between the
probability of increasing events and the influences on that event by changing a
single spin.
