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We use the transport methods developped in [3] to obtain universality resultsfor local statistics of eigenvalues in the bulk and at the edge for$\beta$-matrix models in the multi-cut regime. We construct an approximatetransport map inbetween two probability measures from the fixed fillingfraction model discussed in [6] and deduce from it universality in the initialmodel.

Transport Maps for $\beta$-Matrix Models in the Multi-Cut Regime