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We construct the one matrix model (MM) correlators corresponding to thegeneral bulk-boundary correlation numbers of the minimal Liouville gravity (LG)on the disc. To find agreement between both discrete and continuous approach,we investigate the resonance transformation mixing boundary and bulk couplings.It leads to consider two sectors, depending on whether the matter part of theLG correlator is vanishing due to the fusion rules. In the vanishing case, wedetermine the explicit transformation of the boundary couplings at the firstorder in bulk couplings. In the non-vanishing case, no bulk-boundary resonanceis involved and only the first order of pure boundary resonances have to beconsidered. Those are encoded in the matrix polynomials determined in ourprevious paper. We checked the agreement for the bulk-boundary correlators ofMM and LG in several non-trivial cases. In this process, we developed analternative method to derive the boundary resonance encoding polynomials.

Bulk-boundary correlators in the hermitian matrix model and minimal Liouville gravity