We use the formalism of constrained Gaussian random field to compute a precise large scale simulation of the 60 Mpc/h volume of our Local Universe. We derive the constraints from the reconstructed peculiar velocities of the 2MASS Redshift Survey. We obtain a correlation of 0.97 between the log-density field of the dark matter distribution of the simulation and the log-density of observed galaxies of the Local Universe. We achieve a good comparison of the simulated velocity field to the observed velocity field obtained from the galaxy distances of the NBG-3k. At the end, we compare the two-point correlation function of both the 2MRS galaxies and of the dark matter particles of the simulation. We conclude that this method is a very promising technique of exploring the dynamics and the particularities the Universe in our neighbourhood.
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