Renormalization group and probability theory

The renormalization group has played an important role in the physics of the second half of the 20th 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 1970s. 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.