Lighthouse in Ischia Porto. Photo by Miriam Fiore. |

Some remarkable examples of universality phenomena are:

- the universality of the scaling theory (critical exponents, universal amplitudes, and even finite-size correction coefficients) at a second order phase transition point;
- the universality of the eigenvalue statistics of random matrices;
- the ubiquitous emergence of massless Gaussian free field fluctuations in the theory of dimers, random surfaces, etc.

- the probabilistic and functional analytic methods used to prove the universal behavior of the eigenvalue distribution of Wigner random matrices;
- the constructive renormalization group methods used to compute exact critical exponents in scalar field theories, dimer and spin models;
- the functional analytic methods used for deriving the effective dynamics of stochastic growth interface models;
- the probabilistic and large deviation methods used to control the localization/delocalization transition in pinned polymer models;
- the probabilistic and combinatorial techniques used to control the logarithmic fluctuations of non-harmonic discrete random surfaces.