Kristina Schubert

Spacings in Random Matrix Theory and Repulsive Particle Systems

We consider random matrices from unitary invariant matrix ensembles and more general repulsive particle systems. The considered eigenvalue statistic is the spacing distribution, i.e. the empirical distribution of nearest neighbor spacings. We review some classical results for spacings and establish the convergence of the spacing distribution in a rather strong sense to a universal limiting distribution if the matrix size tends to infinity. Here, we use a non-linear rescaling, called unfolding, to transform the ensemble such that the eigenvalue density is asymptotically constant. The main ingredient for the proof is a strong bulk universality result for correlation functions in the unfolded setting.

Talk recording: https://mediasite.bris.ac.uk/Mediasite/Play/6e93c3fc75d548a6b65708fd63a1878c1d