We use the transport methods developped in [3] to obtain universality results for local statistics of eigenvalues in the bulk and at the edge for β-matrix models in the multi-cut regime. We construct an approximate transport map inbetween two probability measures from the fixed filling fraction model discussed in [6] and deduce from it universality in the initial model.
@article{arxiv.1512.00302,
title = {Transport Maps for $\beta$-Matrix Models in the Multi-Cut Regime},
author = {Florent Bekerman},
journal= {arXiv preprint arXiv:1512.00302},
year = {2017}
}