Universality of the Distribution Functions of Random Matrix Theory

Statistical mechanical lattice models are called solvable if their associated Boltzmann weights satisfy the factorization or star-triangle equations of McGuire [1], Yang [2] and Baxter [3]. For such models the free energy per site and the one-point correlations in the thermodynamic limit are expressible in closed form [4]. There exists a deep mathematical structure [4, 5] underlying these solvable models; and near critical points, a wider applicability than one would initially expect. This last phenomenon, called universality, has its mathematical roots in the strong law of large numbers and the central limit theorems of probability theory and its physical origins in critical phenonmena and conformal field theory.