  We compute the mutual information between finite intervals in two non-compact
2d CFTs in the thermofield double formulation after one of them has been
locally perturbed by a primary operator at some time $t_\omega$ in the large
$c$ limit. We determine the time scale, called the scrambling time, at which
the mutual information vanishes and the original entanglement between the
thermofield double gets destroyed by the perturbation. We provide a holographic
description in terms of a free falling particle in the eternal BTZ black hole
that exactly matches our CFT calculations. Our results hold for any time
$t_\omega$. In particular, when the latter is large, they reproduce the bulk
shock-wave propagation along the BTZ horizon description.
