Markov chain Monte Carlo, or MCMC, is a way to sample probability distributions that cannot be sampled practically using direct samplers. This includes a majority of probability distributions of practical interest. MCMC runs a Markov chain X1, X2, . . ., where Xk+1 is computed from Xk and some other i.i.d. random input. From a coding point of view, a direct solver is X = fSamp();, while the MCM...

Abstract We study the behavior of Lorentzian Engle-Pereira-Rovelli-Livine spinfoam amplitude with homogeneous boundary data, under a graph refinement going from five to twenty tetrahedra. This can be interpreted as wave function Universe, for which we compute geometrical operators, correlation functions, and entanglement entropy. The numerical calculation is made possible by adapting Metropolis...