Abstract:We will report on recent progress regarding the universality of the extreme eigenvalues of a large random matrix with i.i.d. entries. Beyond the radius of the celebrated circular law, we will establish a precise three-term asymptotic expansion for the largest eigenvalue (in modulus) with an optimal error term. Based on this result, we will further show that the properly normalized lar...
PrerequisiteSome knowledge of representation theory of Lie groups or symmetric group and random matrix theory would be helpful. Demonstrations require the use of Python programming language and Sage computer algebra system, so some experience here would be a plus. There is some overlap with material of my previous course "From free fermions to limit shapes and beyond" and connections to the cou...