Spectral statistics beyond Wigner's surmise

08.12.2022 10:30 – 11:30

We will review some basics in random matrix theory, focusing on the three Gaussian ensembles. We will explain what is meant by 'spectrum unfolding' and why it is necessary in order to study local properties of the spectrum. Wigner's surmise is one of these local properties. It gives us a good approximation for the distribution of the nearest-neighbor level spacing in the unfolded spectrum of a random matrix taken from a Gaussian ensemble. Going beyond nearest-neighbor level spacing, we will follow Wigner's footsteps to study the k-th-neighbor spacing distribution, where a simple ansatz can be shown to fit the numerics.

Lieu

Bâtiment: Sciences I

306

entrée libre