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We compute numerically the Lorentzian Engle-Pereira-Rovelli-Livine (EPRL)spinfoam propagator on a 4-simplex, by adapting the methods of Lefschetzthimble and Markov Chain Monte-Carlo to oscillatory spinfoam integrals. Ourmethod can compute any spinfoam observables at relatively large spins. Weobtain the numerical results of the propagators at different spins anddemonstrate their consistency with the expected spinfoam semi-classicalbehavior in the large spin limit. Our results exhibit significant quantumcorrections at smaller spins. Our method is reliable and thus can be employedto discover the semi-classical and quantum behaviors of the spinfoam model.

Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator