  The renormalization group has played an important role in the physics of the
second half of the twentieth century both as a conceptual and a calculational
tool. In particular it provided the key ideas for the construction of a
qualitative and quantitative theory of the critical point in phase transitions
and started a new era in statistical mechanics. Probability theory lies at the
foundation of this branch of physics and the renormalization group has an
interesting probabilistic interpretation as it was recognized in the middle
seventies. This paper intends to provide a concise introduction to this aspect
of the theory of phase transitions which clarifies the deep statistical
significance of critical universality.
