On correlation numbers in 2D minimal gravity and matrix models

We test recent results for the four-point correlation numbers in minimal Liouville gravity against calculations in the one-matrix models, and find full agreement. In the process, we construct the resonance transformation which relates coupling parameters λ_k of the Liouville gravity to the couplings t_k of the matrix models, up to the terms of the order 4. We also conjecture the general form of this transformation.

Talk presented at 'Liouville Gravity and Statistical Models', International conference in memory of Alexei Zamolodchikov, Moscow, 21-24 June 2008.