GAMP/QMATH seminar by Torben Krueger

GAMP (Geometric Analysis and Mathematical Physics)/QMATH Seminar

Speaker: Torben Krueger

Title: Spectral Universality for Random Matrices: From the Global to the Local Scale

Abstract: The spectral statistics of large dimensional self-adjoint random matrices exhibits universal behavior. On the global spectral scale the density of states depends only on the first two moments of the matrix entries, is analytic in the spectral bulk and follows a universal shape at all singular points, i.e. wherever the density vanishes. On the local scale the joint distribution of a finite number of eigenvalues in the bulk or close to a singularity depends only on the symmetry type of the random matrix (Wigner-Dyson-Mehta spectral universality). We present recent results and methods that establish such spectral universality properties from the global down to the smallest spectral scale for a wide range of random matrix models, including matrices with general expectation and correlated entries.