수 학 과

The universality phenomenon has been observed in many contexts of statistical physics. In random matrix theory, the Wigner-Dyson-Mehta universality conjecture asserts that the local eigenvalue statistics of large random matrices are independent of the details of the distribution of the matrix ensemble and only depend on a few universal parameters such as the symmetry class of the matrix. This talk will focus on universality results for the random normal matrix model and the two-dimensional Coulomb gas system. I will give an overview of recent developments on the universality conjecture and explain two approaches to universality based on the asymptotic expansion of orthogonal polynomials and the Ward’s equation from the field theory.