We have studied experimentally the dynamics of the separation of a sheet of paper into two halves in a peeling configuration. The experimental setup consists of a peeling device, where a fracture front is driven along the plane of the paper, with a constant force. The theoretical picture is how an elastic line interacts with a random landscape of fracture toughness. We compare the results with theoretical simulations in several aspects. One recent finding concerns the autocorrelation function of the average front position. The data from the experiments produces so-called cusps or singularities in the correlation function, as predicted by the functional renormalization group theory for elastic lines. Comparisons with simulations with either a short range or a long range elastic kernel demonstrate that the latter agrees with the experimental observations, as expected.